References
Adams D.H.,Semigroups with no nonzero nilpotent elements, Math. Z., 123 (1971), 168–176.
Bosak J.,On radicals of semigroups, Mat.-fyz. časopis, 12 (1962), 230–234.
Bosak J.,On radicals of semigroups, Mat. časopis, 18 (1968), 204–212.
Chick H., B.J. Gardner,The preservation of some ring properties by semilattice sums, Commun. Algebra, 15 (1987), 1017–1038.
Clifford A., G. Preston,The algebraic theory of semigroups, 1964.
Eqbal Ahmed, R. Wiegandt,On lower radicals of semigroups, Math. Nachr., 57 (1973), 163–167.
Fountain J., V. Gould,Completely O-simple semigroups of quotients. II, Contributions to General Algebra, Wien, 1985, 115–124.
Gardner B.J.,Radicals of supplementary semilattice sums of associative rings, Pacif. J. Math., 58 (1975), 387–392.
Grigor R.S.,On semigroups without nilpotent elements, Abstracts of I All-Union simposium on semigroup theory, Sverdlovsk, 1969, p.24 (Russian).
Grigor R.S.,On the theory of radicals of semigroups. I, Mat. Issled. (Kishiniov), 6 (1971), 37–55 (Russian).
Grigor R.S.,On the theory of radicals of semigroups. II, Mat. Issled. (Kishiniov), 8 (1973), 28–46 (Russian).
Hoffman A.E.,Radicals of semigroups with zero, Notices Amer. Math. Soc., 20 (1973), A 359.
Joulain C.,Sur les anneaux non commutatifs. I.Radical, Semin. P. Dubreil, 15 (1963), 1–13.
Kelarev A.V.,Radicals and O-bands of semigroups, preprint (Russian).
Kelarev A.V.,Prevarieties, radicals and bands of associative rings, XVIII All-Union algebraic conference, Kishiniov, 1985, part I, 242 (Russian).
Kelarev A.V.,Radicals of semigroup rings of commutative semigroups, XIX All-Union algebraic conference, Lvov, 1987, part II, 122.
Kelarev A.V.,Radicals and bands of semigroups, Isv. vysh. uch. sav., Matematika (to appear, in Russian).
Kelarev A.V.,Hereditary radicals and bands of associative rings (to appear, in Russian).
Kelarev A.V.,A description of the radicals of semigroup algebras of commutative semigroups (to appear, in Russian).
Kozhevnikov O.B.,On a generalization of the concept of complete regularity, Associativnie dejstvija, 1983, 50–56 (Russian).
Lallement G., M. Petrich,Some remarks concerning completely O-simple semigroups, Bull. Amer. Math. Soc., 70 (1964), 777–778.
Lallement G., M. Petrich,Decompositions I-matricielles d’un demi-grouppe, J. Math. Pures Appl., 45 (1966), 67–117.
Lallement G., M. Petrich,A generalization of the Rees theorem in semigroups, Acta Sci. Math., 30 (1969), 113–132.
Leeuwen L.C.A. van, C. Roos, R. Wiegandt,Characterizations of semisimple classes, J. Austral. Math. Soc., 23 (1977), 172–182.
Luh J.On the concept of radicals of semigroup having kernel, Portugaliae Math., 19 (1960), 189–198.
Marki L.,A note on quasi-ideals and O-matrix decomposition of semigroups with zero, preprint.
Marki L., P.N. Stewart, R. Wiegandt,Radicals and decomposability of semigroups and rings, Annales Univ. Sci. Budapest. Sect. Math., 18 (1975), 27–36.
Marki L.,Structure theorems on certain regular and inverse semigroups, Czechoslovak Math. J., 27 (1977), 388–393.
Marki L.,Radical semisimple classes and varieties of semigroups with zero, Algebraic theory of semigroups, Amsterdam, 1979, 357–369.
Shevrin L.N.,On the general semigroup theory, Mat. Sbornik, 59 (1961), 367–386 (Russian).
Shevrin L.N.,On locally finite semigroups, Sov. Math. Dokl., 162 (1965), 770–773 (Russian).
Steinfeld O.,On semigroups which are unions of completely O-simple subsemigroups, Czehoslovak. Math. J., 16 (1966), 63–69.
Šulka R.,On nilpotent elements, ideals and radicals of a semigroup, Mat.-fys. časopis, 13 (1963), 209–221.
Šulka R.,Note on the Sevrin radical in semigroups, Mat. časopis, 18 (1968), 57–58.
Weissglass J.,Semigroup rings and semilattice sums of rings, Proc. Amer. Math. Soc., 39 (1973), 471–478.
Wiegandt R.,On the structure of lower radical semigroups, Czechoslovak Math. J., 22 (1972), 1–6.
Author information
Authors and Affiliations
Additional information
Communicated by L.N. Shevrin
Rights and permissions
About this article
Cite this article
Kelarev, A.V. Hereditary radicals and O-bands of semigroups. Semigroup Forum 38, 57–76 (1989). https://doi.org/10.1007/BF02573218
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02573218