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Semigroups and their subsemigroup lattices

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References

  • [Ar 1] ARSHINOV, M.N. (М.Н. Аршинов)Lattice isomorphisms of certain groups decomposable into a free product, Mat. Zap. Krasnoyarsk. Pedagog. Inst., 3 (1970), 74–86 (in Russian).

    Google Scholar 

  • [Ar 2] —On projectivities of pure supersolvable groups, Dokl. Akad. Nauk Belorussia SSR, 14, No. 11 (1970), 984–985 (in Russian).

    MATH  Google Scholar 

  • [Ar 3] —On lattice isomorphisms of mixed nilpotent groups, Trudy Zon. Objed. Math. Kafedr Pedagog. Inst. Sibiri, 2 (1972), 8–29 (in Russian).

    Google Scholar 

  • [Ar 4] —Lattice isomorphisms of certain solvable torsion-free groups, Trudy Mosk. Inst. Inj. Transp., 385 (1971), 125–141 (in Russian).

    Google Scholar 

  • [Ar-Sa] ARSHINOV, M.N. and L.E. SADOVSKIÎ (М.Н. Аршинов, Л.Е. Садовский)Certain lattice-theoretic properties of groups and semigroups, Usp. Mat. Nauk, 27, No. 6 (1972), 139–180 (in Russian).

    Google Scholar 

  • [Baer 1] BAER, R.The significance of the system of subgroups for the structure of the group, Amer. J. Math., 61 (1939), 1–44.

    Article  MATH  MathSciNet  Google Scholar 

  • [Baer 2] BAER, R.Linear Algebra and Projective Geometry, New York, 1952; Russian transl. Moscow, 1955.

  • [Ba 1] BARANSKIÎ, V.A. (В.А. Баранский)Lattice isomorphisms of semigroups decomposable into a free product with amalgamated zero, Mat. Sbornik, 83, No.2 (1970), 155–164 (in Russian).

    Google Scholar 

  • [Ba 2] —Lattice isomorphisms of finitely presented semigroups, Mat. Zametki, 12, No.5 (1972), 591–600 (in Russian).

    MathSciNet  Google Scholar 

  • [Ba 3] BARANSKIÎ., V.A. (В.А. Баранский)On lattice isomorphisms of semigroups with one defining relation, Reports of All-Union algebraic simpos., Homel, 1975, 193 (in Russian).

  • [Ba 4] —Lattice isomorphisms of commutative Archimedean semigroups without idempotents, Mat., Zap. Ural. Univ., Sverdlovsk, 9, No.3 (1975), 8–13 (in Russian)

    Google Scholar 

  • [Ba 5] —On lattice isomorphisms of nilpotent semigroups, Izv. vysh. uch. zav. Matematika, 3 (1979), 3–11 (in Russian).

    Google Scholar 

  • [Ba-Tr, 1] BARANSKIÎ, V.A. and A.N. TRAKHTMAN (В.А. Баранский, А.Н. Трахтман)Half-isomorphisms of matrix bands of cancellative semigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 6, No.3 (1968), 1–11 (in Russian).

    Google Scholar 

  • [Ba-Tr, 2] —Lattice isomorphisms of matrix bands of aperiodic commutative cancellative semigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 7, No. 1 (1969), 3–22 (in Russian).

    Google Scholar 

  • [Ba-Tr,3] —On subsemigroup graphs, Mat. Časopis, 20, No.3 (1970), 135–140 (in Russian).

    Google Scholar 

  • [Bi 1] BIRKHOFF, G.Lattice Theory, Amer. Math. Soc., 2nd edition, 1948; Russian Transl., Moscow, 1952.

  • [Bi 2] BIRKHOFF, G.Lattice Theory, Amer. Math. Soc., 3rd edition, 1967.

  • [Bor 1] BORISOV, A.A. (А.А. Борисов)Lattice isomorphisms of semigroups of directed transformations and directed endomorphisms of posets, VINITI, N 2018-75 DEP, Ref. J. Mat., 11A237 DEP (in Russian).

  • [Bor 2] —On lattice isomorphisms of semigroups of partial transformations, Sovremen. Algebra, Leningrad. Pedagog. Inst., 6 (1977), 33–52 (in Russian).

    Google Scholar 

  • [Bor 3] —On lattice isomorphisms of semigroups of full transformations, Sovremen. Algebra, Leningrad. Pedagog. Inst., 6 (1977), 53–65 (in Russian).

    Google Scholar 

  • [Bor 4] BORISOV, A.A. (А.А. Борисов)On the question about lattice isomorphisms of semigroups with one defining relation, Reports of II All-Union sympos. on semigroup theory, Sverdlovsk, 1978, 12 (in Russian).

  • [Bor 5] BORISOV, A.A. (А.А. Борисов)Lattice determinability of a certain class of commutative semigroups without idempotents, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 16–17 (in Russian).

  • [Bos 1] BOSAK, J. B-pologrupy, Mat-fyz. Časopis, 2, No. 1 (1961), 32–44 (in Czech).

    Google Scholar 

  • [Bos 2] BOSAK, J.The graphs of semigroups, Proc. of the sympos. held in Smolenice, June 1963, Praha, 1964, 119–125.

  • [Bos 3] —On subsemigroups of semigroups, Mat-fyz. Časopis, 14, No. 4 (1964), 289–296.

    MathSciNet  MATH  Google Scholar 

  • [Cl-Petr] CLIFFORD, A.H. and M. PETRICHSome classes of completely regular semigroups, J. Algebra, 46 No. 2 (1977), 462–480.

    Article  MATH  MathSciNet  Google Scholar 

  • [Cl-Pr] CLIFFORD, A.H. and G.B. PRESTONThe Algebraic Theory of Semigroups, Amer. Math. Soc., Vol. 1, 1961, Vol. 2, 1967; Russian transl., Vol. 1,2, Moscow, 1972.

  • [Ego 1] EGO, M.Strusture des demi-groupes dont le treillis des sous-demi-groupes est distributif, C.r. Acad. Sci., 252, No. 17 (1961), 2490–2492.

    MATH  MathSciNet  Google Scholar 

  • [Ego 2] —Structure des demi-groupes dont le treillis des sous-demi-groupes est modulaire ou semi-modulaire, C.r. Acad. Sci., 254, No. 10 (1962), 1723–1725.

    MATH  MathSciNet  Google Scholar 

  • [Ego 3,3′] —Structure des demi-groupes dont le treillis des sous-demi-groupes satisfait aux conditions \(\bar C_2 \), C2,\(\bar C_1 \),ou C1 a la semimodularite affaiblie ou a la modularite affaiblie, C.r. Acad. Sci., 255 (1962), 1840–1842, 2699–2701.

    MathSciNet  Google Scholar 

  • [Ego 4] —Structure des demi-groupes dont le treillis des sous-demi-groupes satisfait a certaines conditions, Bul. Math. Soc. France, 91, No.2 (1963), 137–201.

    MATH  MathSciNet  Google Scholar 

  • [Er 1] ERSHOVA, T.I. (Т.И. Ершова)Inverse semigroups with certain types of inverse subsemigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 7, No.1 (1969), 62–76 (in Russian).

    MATH  Google Scholar 

  • [Er 2] —Determinability of monogenic inverse semigroups by the lattice of inverse subsemigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 8, No.1 (1971), 44–49 (in Russian).

    Google Scholar 

  • [Er 3] ERSHOVA, T.I. (Т.И. Ершова)On the lattice of inverse subsemigroups of monogenic inverse semigroups, Reports of XI All-Union algebraic colloq., Kishinev, 1971, 195 (in Russian).

  • [Er 4] —Lattice isomorphisms of inverse semigroups, Izv. vysh. uch. zav. Matematika, 9 (1972), 25–32 (in Russian).

    Google Scholar 

  • [Er 5] ERSHOVA, T.I. (Т.И. Ершова)Projectivities of inverse semigroups, Reports of All-Union algebraic sympos., Homel, 1975, 212 (in Russian).

  • [Er 6] —Inverse semigroups with certain finiteness conditions, Izv. vysh. uch. zav. Mathematika, 11 (1977), 7–14 (in Russian).

    Google Scholar 

  • [Er 7] ERSHOVA, T.I. (Т.И. Ершова)Projectivities of Brandt semigroups, Reports of II All-Union sympos. on semigroup theory, Sverdlovsk, 1978, 26 (in Russian).

  • [Er 8] ERSHOVA, T.I. (Т.И. Ершова)Projectivities of inverse semigroups, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 54 (in Russian).

  • [Ev 1] EVSEEV, A.E. (А.Е. Евсеев)Lattice properties of a certain semigroup of endomorphisms of a poset, Mat. Sbornik, 65, No. 2 (1964), 151–171 (in Russian).

    MathSciNet  Google Scholar 

  • [Ev 2] —Semigroups with ordinal decomposable semilattices of subsemigroups, Izv. vysh. uch. zav. Matematika, 6 (1965), 74–84 (in Russian).

    MathSciNet  Google Scholar 

  • [Ev 3] —On certain classes of semigroups with ordinal decomposable semilattices of subsemigroups, Uch. Zap. Leningrad. Pedagog. Inst., 302 (1967), 63–69 (in Russian).

    MathSciNet  Google Scholar 

  • [Ev 4] —On the semilattice of finitely generated subsemigroups of a semigroup, Uch. Zap. Leningrad. Pedagog. Inst., 328 (1967), 87–93 (in Russian).

    MathSciNet  Google Scholar 

  • [Ev 5] —On lattice isomorphousness of semigroups with zero and semigroups with unit, Uch. Zap. Leningrad. Pedagog. Inst., 387 (1968), 87–93 (in Russian).

    MathSciNet  Google Scholar 

  • [Ev 6] —Lattice isomorphisms of free nilpotent semigroups, Uch. Zap. Leningrad. Pedagog. Inst., 387 (1968), 112–125 (in Russian).

    MathSciNet  Google Scholar 

  • [Fi] FILIPPOV, N.D. (Н.Д. Филиппов)Projectivities of lattices, Mat. Sbornik, 70, No. 1 (1966), 36–54 (in Russian).

    Google Scholar 

  • [Fu] FUCHS, L.Abelian groups, Budapest, 1958.

  • [Je-Mi] JENSEN, B.A. and D.W. MILLERCommutative semigroups which are almost finite, Pacific J. Math., 27 (1968), 533–538.

    MATH  MathSciNet  Google Scholar 

  • [Jo 1] JONES, P.R.Semimodular inverse semigroups, J. London Math. Soc., 17, No. 3 (1978), 446–456.

    Article  MATH  MathSciNet  Google Scholar 

  • [Jo 2] —Distributive inverse semigroups, J. London Math. Soc., 17, No. 3 (1978), 457–466.

    Article  MATH  MathSciNet  Google Scholar 

  • [Jo 3] —Lattice isomorphisms of inverse semigroups, Proc. Edinburgh Math. Soc., 21, No. 2 (1978), 149–157.

    MATH  MathSciNet  Google Scholar 

  • [Jo 4] —Lattice isomorphisms of distributive semigroups, Quart. J. Math., 30, No. 119 (1979), 301–314.

    Article  MATH  MathSciNet  Google Scholar 

  • [Jo 5] —Inverse semigroups determined by their lattices of inverse subsemigroups, Czech. Math. J., 106 (1981), 24–47; J. Austral. Math. Soc., 30 (1981), 321–346.

    Google Scholar 

  • [Jo 6] —Inverse semigroups whose full inverse subsemigroups form a chain, Glasgow Math. J., 22, No. 2 (1981), 159–165.

    MATH  MathSciNet  Google Scholar 

  • [Jón] JÓNSSON, B.Topics in universal algebra, Lect. Notes Math., v. 250, 1972.

  • [Ka 1] KACMAN, S.I. (С.И. Кацман)Semigroups whose subsemigroup lattices are complemented, Sib. Mat. J., 15, No.6 (1974), 1276–1285 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Ka 2] —On periodic K-semigroups, Sib. Mat. J., 19, No.6 (1978), 1357, VINITI, N 1136-78 DEP (in Russian).

    MATH  Google Scholar 

  • [Ka 3] —On periodic K-semigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 11, No.3 (1979), 54–61 (in Russian).

    MathSciNet  Google Scholar 

  • [Ka 4] —Commutative semigroups with self-dual lattice of subsemigroups, Semigroup Forum, 18 (1979), 119–161.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ka 5] KACMAN, S.I. (С.И. Кацман)Semigroups with decomposable into a direct product semilattices of subsemigroups, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 65 (in Russian).

  • [Ka 6] KACMAN, S.I. (С.И. Кацман)Commutative semigroups with the maximal condition for subsemigroups, Report on the meeting 243 of the Seminar “Semigroups and other algebraic systems”, Sverdlovsk, 12.05.1976 (in Russian).

  • [Kar] KARGAPOLOV, M.I. (М.И. Каргаполов)On the elementary theory of subgroup lattices, Algebra i Logika. Seminar, Novosibirsk, 1, No.3 (1962), 157–161 (in Russian).

    MathSciNet  Google Scholar 

  • [Ki] KIZNER, F.I. (Ф.И. Кизнер)Lattice isomorphisms of free products of semigroups with unit and with zero, Mat. Sbornik, 13, No. 2 (1966), 251–256 (in Russian).

    MathSciNet  Google Scholar 

  • [Kon-Kut] KONTOROVICH, P.G. and K.M. KUTYEV (П.Г. Конторович, К.М. Кутыев)Symmetric lattices, Sib. Mat. J. 10, No. 3 (1969), 537–548 (in Russian).

    Google Scholar 

  • [Kon-Pek-Sta] KONTOROVICH, P.G. and A.S. PEKELIS and A.I. STAROSTIN (П.Г. Конторович, А.С. Пекелис, А.И. Старостин)Structure questions of group theory, Mat. Zap. Ural. Univ., Sverdlovsk, 3, No.1 (1961), 3–50 (in Russian).

    Google Scholar 

  • [Ko] KONTOROVICH, P.G. and A.S. PEKELIS and A.I. STAROSTIN (П.Г. Конторович, А.С. Пекелис, А.И. Старостин)Kourovka Notebook (unsolved problems of group theory) 7th edition, Novosibirsk, 1980 (in Russian, some problems in English).

  • [Kut 1] KUTYEV, K.M. (К.М. Кутыев) ΠC-isomorphisms of partially ordered locally nilpotent groups, Usp. Mat. Nauk, 11, No. 2 (1956), 193–198 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Kut 2] — ΠC-isomorphism of ordered groups, Izv. Akad. Nauk SSSR, ser. mat., 24 (1960), 807–824 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Kut 3] — ΠC-isomorphism of an ordered group, Dokl. Akad. Nauk SSSR, 135, No. 6 (1960), 1326–1329 (in Russian).

    MathSciNet  Google Scholar 

  • [Kut 4] —On ΠC-isomorphism of certain classes of R-groups, Izv. Akad. Nauk SSSR, ser. mat., 27, No. 4 (1963), 701–722 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Kut 5] —A remark on ΠC-isomorphism of R-groups which locally satisfy the condition (N), Ukr. Mat. J., 16, No. 4 (1964), 534–536 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Kut 6] — ΠC-isomorphism of a lattice-ordered group, Dokl. Akad. Nauk SSSR, 179, No. 4 (1968), 775–778 (in Russian).

    MathSciNet  Google Scholar 

  • [Kut 7] — ΠC-isomorphism of a lattice-ordered group, Mat. Zametki, 7, No.5 (1970), 537–544 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Kut 8] —On certain lattice properties of subsemigroups within a group, Dokl. Akad. Nauk SSSR, 178, No.2 (1968), 286–290 (in Russian).

    MathSciNet  Google Scholar 

  • [Kut 9] —On certain lattice properties of subsemigroups within a group, Sib. Mat. J., 12, No. 4 (1971), 785–804 (in Russian).

    MathSciNet  Google Scholar 

  • [Kut 10] KUTYEV, K.M. (К.М. Кутыев)A subsemigroup-lattice criterion of the commutativity of an 1-group, VINITI, N 3191-79 DEP, Ref. J. Mat., 1980, 1A234 DEP (in Russian).

  • [Kut 11] KUTYEV, R.M. (К.М. Кутыев)A subsemigroup-lattice characteristic of an 1-group, VINITI, N 3192-79 DEP, Ref. J. Mat., 1980, 1A235 DEP (in Russian).

  • [Kut 12] KUTYEV, K.M. (К.М. Кутыев)On the subsemigroup lattice of the ordered group of real numbers, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 200 (in Russian).

  • [Kuz 1] KUZNETSOV, V.I. (В.И. Кузнецов)On lattice isomorphisms of certain semigroups, Izv. Akad. Nauk Ukrainian SSR, 11 (1964), 1423–1426 (in Ukraine)

    Google Scholar 

  • [Kuz 2] —On lattice isomorphisms of completely simple semigroups, Izv. Akad. Nauk Ukrainian SSR, 12 (1964), 1578–1581 (in Ukraine).

    Google Scholar 

  • [Li 1] LIBERMAN, A.A. (А.А. Либерман)Lattice isomorphisms of monogenic inverse semigroups, Reports of II All-Union sympos. on semigroup theory, Sverdlovsk, 1978, 51 (in Russian).

  • [Li 2] —Lattice isomorphisms of cyclic semigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 12, No.1 (1980), 99–110 (in Russian).

    MathSciNet  Google Scholar 

  • [Lin] LIN Y.F.A problem of Bosak concerning the graphs of semigroups, Proc. Amer. Math. Soc., 22 (1969), 343–346.

    Article  Google Scholar 

  • [Lja] LJAPIN, E.S. (Е.С. Ляпин)Semigroups, Moscow, 1960 (in Russian); 3rd edition, Amer. Math. Soc. Transl., 1974.

  • [Ma 1] MALCEV, A.I. (А.И. Мальцев)Algebraic systems, Moscow, 1970 (in Russian); Transl. New York, 1973.

  • [Ma 2] —Nilpotent semigroups, Uch. Zap. Ivanov. Pedagog. Inst., 4 (1953), 107–111; Izbr. Trudy, Moscow, 1976, Vol. 1, 335–339 (in Russian).

    MathSciNet  Google Scholar 

  • [Ma 3] —On multiplication of classes of algebraic systems, Sib. Mat. J., 8, No.2 (1967), 346–365; Izbr. Trudy, Moscow, 1976, Vol. 2, 355–372 (in Russian).

    MathSciNet  Google Scholar 

  • [McK] McKENZIE, R.Semigroups whose proper subsemigroups have lesser power, Algebra Univ., 1, No.1 (1971), 21–25.

    Article  MATH  MathSciNet  Google Scholar 

  • [McL] McLEAN, D.Idempotent semigroups, Amer. Math. Monthly, 61, No. 2 (1954), 110–113.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ols 1] OLSHANSKIÎ, A.Ju. (А.Ю. Ольшанский)Infinite groups with cyclic subgroups, Dokl. Akad. Nauk SSSR, 245, No. 4 (1979), 785–737 (in Russian).

    MathSciNet  Google Scholar 

  • [Ols 2] —Infinite group with subgroups of prime orders, Izv. Akad. Nauk SSSR, ser. mat., 44, No.2 (1980), 309–321 (in Russian).

    MathSciNet  Google Scholar 

  • [Ov 1] OVSYANNIKOV, A.J. (А.Я. Овсянников)Lattice isomorphisms of commutative semigroups with one defining relation, Mat. Zap. Ural. Univ., Sverdlovsk, 10, No. 3 (1977), 138–172 (in Russian).

    Google Scholar 

  • [Ov 2] —On lattice isomorphisms of relatively free semigroups, Mat. Zametki, 21, No. 4 (1977), 459–461 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Ov 3] OVSYANNIKOV, A.J.Lattice isomorphisms of semigroups decomposable into a free product in varieties of idempotent semigroups and commutative semigroups, VINITI, N 2787-79 DEP, Ref. J. Mat., 1979, 10A108 DEP (in Russian).

  • [Ov 4] —On lattice isomorphisms of finitely presented nilsemigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 11, No. 1 (1978), 137–144 (in Russian).

    MathSciNet  Google Scholar 

  • [Ov 5] —On lattice isomorphisms of aperiodic cancellative semigroups, Izv. vysh. uch. zav. Matematika, 3 (1980), 32–44 (in Russian).

    MathSciNet  Google Scholar 

  • [Ov 6] —Lattice isomorphisms of commutative relatively free semigroups, Semigroup Forum, 20 (1980), 189–225.

    Article  MATH  MathSciNet  Google Scholar 

  • [Ov 7] OVSYANNIKOV, A.J.On lattice isomorphisms of free products in varieties of nilsemigroups, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 99 (in Russian).

  • [Ov 8] —Lattice isomorphisms of commutative semigroups with one defining relation, II. Mat. Zap. Ural. Univ., Sverdlovsk, 12, No. 3 (1981), 90–107 (in Russian).

    MathSciNet  Google Scholar 

  • [Pek] PEKELIS, A.S. (А. С. Пекелис)On groups with isomorphic subsemigroup lattices, Izv. vysh. uch. zav. Matematika, 1 (1957), 189–194 (in Russian).

    MathSciNet  Google Scholar 

  • [Petrich 1] PETRICH, M.A remark on result of Kacman (preprint), Pennsylvania State Univ., 1975, 33 pp.

  • [Petrich 2] PETRICH, M.Lectures in semigroups, Berlin, 1977.

  • [Pe 1] PETROPAVLOVSKAYA, R.V. (Р. В. Петропавловская)On decomposability into a direct sum of the sub-system lattice of an associative system, Dokl. Akad. Nauk SSSR, 81, No. 5 (1951), 999–1001 (in Russian).

    MathSciNet  Google Scholar 

  • [Pe 2] —On determinability of a group by its subsystem lattice, Mat. Sbornik, 29, No. 1 (1951), 63–68 (in Russian).

    MathSciNet  Google Scholar 

  • [Pe 3] —Lattice isomorphisms of free associative systems, Mat. Sbornik, 28, No. 3 (1951), 586–602 (in Russian).

    MathSciNet  Google Scholar 

  • [Pe 4] —Associative systems which are lattice-isomorphic to groups, I, II, III, Vestnik Leningrad. Univ., 13, (1956), 5–25, 19 (1956), 80–99, 19 (1957), 5–19 (in Russian).

    MathSciNet  Google Scholar 

  • [Pe 5] —On a certain class of groups which are determined by subsemigroup lattices, Mat. Sbornik, 66, No. 2 (1965), 265–271 (in Russian).

    Google Scholar 

  • [Pe 6] —A description of the structure of semigroups which are lattice-isomorphic to groups of a certain class, Vestnik Leningrad. Univ., 7 (1967), 150–153 (in Russian).

    Google Scholar 

  • [Plo 1] PLOTKIN, B. I. (Б. И. Плоткин)Radical and semisimple groups, Trudy Mosk. Mat. Obsh., 6 (1957), 299–337 (in Russian).

    MathSciNet  MATH  Google Scholar 

  • [Plo 2] —Generalized solvable and generalized nilpotent groups, Usp. Mat. Nauk, 13, No. 4 (1958), 89–172 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Po] PONDELICEK, B.Diameter of a semigroup graph, Casopis pestov. mat., 92 (1967), 206–211 (in Czech).

    MathSciNet  MATH  Google Scholar 

  • [Sa 1] SADOVSKIÎ, L. E. (Л. Е. Садовский)On lattice isomorphisms of free products of groups, Mat. Sbornik, 21 (1947), 63–82 (in Russian).

    Google Scholar 

  • [Sa 2] —Certain lattice-theoretic questions of group theory, Usp. Mat. Nauk, 23, No. 3 (1968), 123–158 (in Russian).

    Google Scholar 

  • [Sc] SCOTT D.W.Half-isomorphisms of groups, Proc. Amer. Math. Soc. 8, No. 6 (1957), 1141–1144.

    Article  MathSciNet  Google Scholar 

  • [Sha 1] SHARKOV, Ju. A. (Ю. А. Шарков)On lattice properties of completely regular semigroups, VINITI, N 1140-75 DEP, Ref. J. Mat., 1975. 8A217 DEP (in Russian).

  • [Sha 2] —Half-isomorphisms of completely simple semigroups, Izv. Akad. Nauk Azerbaijan SSR, ser. fiz.-mat. nauki, 2 (1975), 112–115 (in Russian).

    Google Scholar 

  • [Sha 3] —On lattice isomorphisms of completely simple semigroups, Isv. vysh. uch. zav. Matematika, 4 (1978), 124–126 (in Russian).

    Google Scholar 

  • [Sha 4] SHARKOV, Ju. A. (Ю. А. Шарков)Certain lattice properties of completely O-simple semigroups, Spec. voprosy algebra i topolog., Baku, 1980, 91–104 (in Russian).

  • [Sha 5] SHARKOV, Ju. A. (Ю. А. Шарков)Lattice isomorphisms of completely simple semigroups, VINITI, N 3413-81, Ref. J. Mat., 1981, 11A148 DEP (in Russian).

  • [Sha 6] SHARKOV, Ju. A. (Ю. А. Шарков)On strict lattice determinability of completely simple semigroups, Reports of XVI All-Union algebraic conference, Leningrad, 1981, part 2, 146 (in Russian).

  • [Shev 1] SHEVRIN, L.N. (Л. Н. Шеврин)A contribution to the general theory of semigroups, Mat. Sbornik, 53, No. 3 (1961), 367–386 (in Russian).

    Google Scholar 

  • [Shev 2] SHEVRIN, L. N.On lattice properties of semigroups, Dokl. Akad. Nauk SSSR, 138, No. 1 (1961), 73–76 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 3] —Semigroups with certain types of subsemigroup lattices, Dokl. Akad. Nauk SSSR, 138, No. 4 (1961). 796–798 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 4] —On semigroups all of whose subsemigroups are nilpotent, Sib. Mat. J., 2, No. 6 (1961), 936–942 (in Russian).

    MATH  Google Scholar 

  • [Shev 5] —Nilsemigroups with certain finiteness conditions, Mat. Sbornik, 55, No. 4 (1961), 473–480 (in Russian).

    Google Scholar 

  • [Shev 6] —Semigroups whose subsemigroup lattices are relatively complemented, Dokl. Akad. Nauk SSSR, 144, No. 1 (1962), 72–75 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 7] —On lattice properties of semigroups, Sib. Mat. J., 3, No. 3 (1962), 446–470 (in Russian).

    MATH  Google Scholar 

  • [Shev 8] —Semigroups whose subsemigroup lattices are uniquely complemented, Sib. Mat. J., 4, No. 3 (1963), 709–711 (in Russian).

    MATH  Google Scholar 

  • [Shev 9] —Semigroups with Dedekind 1) subsemigroup lattices, Dokl. Akad. Nauk SSSR, 148, No. 2 (1963), 292–295 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 10] —On semigroups all of whose subsemigroups are achievable, Mat. Sbornik, 61, No. 2 (1963), 253–256 (in Russian).

    Google Scholar 

  • [Shev 11] —A subsemigroup-lattice characteristic of orderable groups, Usp. Mat. Nauk, 19, No. 5 (1964), 157–161 (in Russian).

    MATH  Google Scholar 

  • [Shev 12] —Lattice isomorphisms of commutative aperiodic cancellative semigroups, Mat. Sbornik, 63, No. 1 (1964), 43–58 (in Russian).

    Google Scholar 

  • [Shev 13] —A subsemigroup-lattice characteristic of commutative aperiodic groups, Sib. Mat. J., 5, No. 3 (1964), 671–678 (in Russian).

    MATH  Google Scholar 

  • [Shev 14] —Basic problems in the theory of projectivities of semilattices. Mat. Sbornik, 66, No. 4 (1965), 568–597 (in Russian).

    Google Scholar 

  • [Shev 15] —Lattice properties of idempotent semigroups, I, Sib. Mat. J., 6, No. 2 (1965), 459–474 (in Russian).

    MATH  Google Scholar 

  • [Shev 16] —On isomorphousness of semigroups with relatively complemented subsemigroups, Mat. Zap. Ural. Univ., Sverdlovsk, 5 (1965), 92–100 (in Russian).

    MATH  Google Scholar 

  • [Shev 17] —Strong bands of semigroups, Izv. vysh. uch. zav. Matematika, 6 (1965), 156–165 (in Russian).

    Google Scholar 

  • [Shev 18] SHEVRIN, L.N.Semigroups of finite breadth, Theory of semigroups and its applications, Saratov. Univ., issue 1 (1965), 325–351 (in Russian).

    MATH  Google Scholar 

  • [Shev 19] —Certain finiteness conditions in theory of semigroups, Izv. Akad. Nauk SSSR, ser. mat., 29, No. 3 (1965), 553–566 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Shev 20] —On lattice isomorphisms of commutative holoids, Izv. vysh. uch. zav. Matematika, 1 (1966), 153–160 (in Russian).

    Google Scholar 

  • [Shev 21] —Lattice properties of idempotent semigroups, II, Sib. Mat. J., 7, No. 2 (1966), 437–454 (in Russian).

    Google Scholar 

  • [Shev 22] —On elementary lattice properties of semigroups, Dokl. Akad. Nauk SSSR, 167, No. 2 (1966), 305–308 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 23] —Elementary lattice properties of semigroups, Sib. Mat. J., 7, No. 3 (1966), 664–684 (in Russian).

    MATH  Google Scholar 

  • [Shev 24] —Basic problems in the theory of projectivities of semilattices, II, Mat. Zap. Ural. Univ., Sverdlovsk, 5, No. 3 (1966), 107–122 (in Russian).

    MATH  Google Scholar 

  • [Shev 25] SHEVRIN, L. N.Lattice properties of semigroups, Dissertation for Doctor of Science, Sverdlovsk, 1966, 346 pp. (in Russian).

  • [Shev 26] —Half-isomorphisms of cancellative semigroups, Izv. Akad. Nauk SSSR, ser. mat., 31, No. 5 (1967), 957–964 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev 27] —On lattice isomorphisms of orderable cancellative semigroups, Izv. Akad. Nauk SSSR, ser. mat., 31, No. 6 (1967), 1229–1238 (in Russian).

    MATH  MathSciNet  Google Scholar 

  • [Shev 28] —On the subsemigroup lattice of a group as a symmetric lattice, Mat. Zap. Ural. Univ., Sverdlovsk, 7, No. 3 (1970), 234–238 (in Russian).

    MATH  Google Scholar 

  • [Shev 29] —A supplement to the paperSemigroups of finite breadth”, Theory of semigroups and its applications, Saratov. Univ., issue 2 (1970), 94–96 (in Russian).

    Google Scholar 

  • [Shev 30] —A certain general theorem on semigroups with some finiteness conditions, Mat. Zametki, 5, No. 6 (1974), 925–935 (in Russian).

    Google Scholar 

  • [Shev 31] —A contribution to the theory of periodic semigroups, Izv. vysh. uch. zav. Matematika, 5 (1974), 205–216 (in Russian).

    Google Scholar 

  • [Shev-Ba] SHEVRIN, L.N. and V. A. BARANSKII (Л. Н. Шеврин, В. А. Баранский)Lattice isomorphisms of semigroups decomposable into a free product, Mat. Sbornik, 71, No. 2 (1966), 236–250 (in Russian).

    Google Scholar 

  • [Shev-Be] SHEVRIN, L.N. and L.M. BESHKETO (qL.Н. Шеврин, Л.М. Бешкето)Idempotent semigroups whose subsemigroups semilattices are decomposable into a direct product, Uch. Zap. Sverdlovsk. Pedagog. Inst., 124 (1970), 82–87 (in Russian).

    Google Scholar 

  • [Shev-Kop, 1] SHEVRIN, L.N. and V.M. KOPYTOV (Л.Н. Шеврин, В.М. Копытов)Semigroups with relatively complemented subsemigroups, Dokl. Akad. Nauk SSSR, 145, No. 5 (1962), 1012–1015 (in Russian).

    MathSciNet  Google Scholar 

  • [Shev-Kop, 2] SHEVRIN, L.N. and V.M. KOPYTOV (Л.Н. Шеврин, В.М. Копытов)Semigroups whose subsemigroup semilattices have relative complements, Mat. Zap. Ural. Univ., Sverdlovsk, 4, No. 1 (1963), 74–83 (in Russian).

    MATH  Google Scholar 

  • [Shev-Pro] SHEVRIN, L.N. and V.M. POPYTOV (Л.Н. Шеврин, В.М. Копытов)Semigroups with isotone idealizer function, Trudy Mosk. Mat. Obsh., 29 (1973), 235–246 (in Russian).

    MATH  Google Scholar 

  • [Shu] SHUNKOV, V.P. (В.П. Шунков)On locally finite groups with the minimal condition for abelian subgroups, Algebra i Logika. Seminar, Novosibirsk, 9, No. 5 (1970), 579–615 (in Russian).

    Google Scholar 

  • [Sko 1] SKORNYAKOV, L.A. Л.А. Скорняков)Projective mappings of modules, Izv. Akad. Nauk SSSR, ser. mat., 24, No. 3 (1960), 511–520 (in Russian).

    MathSciNet  MATH  Google Scholar 

  • [Sko 2]Complemented Dedekind lattices and regular rings, Moscow, 1960 (in Russian); Transl. Edinburgh-London, 1964.

  • [Su] SUZUKI, M.Structure of a group and the structure of its lattice of subgroups, Berlin Gottingen Heidelberg, 1956; Russian transl. Moscow, 1960.

  • [Sv 1] SUZUKI, M.The Sverdlovsk Notebook (unsolved problems of semigroup theory, Sverdlovsk, 1969 (in Russian).

  • [Sv 1’] SUZUKI, M.The Sverdlovsk Tetrad, (English transl. of [Sv 1]) Semigroup Forum, 4 (1972), 274–280.

    Article  MathSciNet  Google Scholar 

  • [Sv 2] SUZUKI, M.The Sverdlovsk Notebook (unsolved problems of semigroup theory), 2nd edition, Sverdlovsk, 1979 (in Russian).

  • [Ta 1] TAMURA, T.On a monoid whose submonoids form a chain, J. Gakugei Tokushima Univ., 5 (1954), 8–16.

    Google Scholar 

  • [Ta 2] TAMURA, T.On semigroups whose subsemigroup lattice is the Boolean algebra of all subsets of a set, J. Gakugei Tokushima Univ., 12 (1962), 1–4.

    Google Scholar 

  • [Ta 3] TAMURA, T.Note on *-semigroups, Proc. Amer. Math. Soc., 9 (1962), 505–508.

    Google Scholar 

  • [Ta 4] TAMURA, T.Semigroups and their subsemigroup lattices, Pacific J. Math. 13 (1963), 725–735.

    MATH  MathSciNet  Google Scholar 

  • [Tr] TRAKHTMAN, A.N. (А.Н. Трахтман)Subsemigroup graphs and subsemigroup lattices, Izv. vysh. uch. zav. Matematika, 21 (1976), 69–78 (in Russian).

    MathSciNet  Google Scholar 

  • [Ush] USHAKOV, V.I. (В.И. Ушаков)Lattice-system isomorphisms of aperiodic locally nilpotent groups, Izv. vysh. uch. zav. Matematika, 1 (1957), 223–226 (in Russian).

    Google Scholar 

  • [Va] VAGNER, V.D. (В.Д. Вагнер)Semigroups with self-dual subsemigroup lattices, Diploma, Sverdlovsk. Pedagog. Inst., 1973 (in Russian).

  • [Ze] ZELINKA, В.Diameter of the graph of proper subsemigroups of a commutative semigroup, Mat-fyz. Casopic, 15 (1965), 143–145 (in Czech).

    MathSciNet  MATH  Google Scholar 

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Dedicated to Professors Alfred H. CLIFFORD patriarch in semigroups, on the occasion of his 75th birthday Garrett BIRKHOFF patriarch in lattices, on the occasion of his 72nd birthday in 1983

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Shevrin, L.N., Ovsyannikov, A.J. Semigroups and their subsemigroup lattices. Semigroup Forum 27, 1–154 (1983). https://doi.org/10.1007/BF02572737

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