This is a preview of subscription content, log in via an institution to check access.
Literature Cited
V. A. Artamonov, Universal Algebras [in Russian], Itogi Nauki: Algebra, Topologiya, Geometriya, Vol. 14, VINITI (1976).
J. Kalicki and D. Scott, “Equational completeness of abstract algebras,” Proc. Koninkl. Nederl. Akad. Wetensch.,A58, No. 5, 650–659 (1955).
A. Tarski, “Equationally complete rings and relation algebras,” Proc. Koninkl. Nederl. Akad. Wetensch.,A59, No. 1, 39–46 (1956).
W. F. Page and A. T. Butson, “The lattice of equational classes of m-semigroups,” Algebra Univers.,3, No. 1, 112–126 (1973).
W. F. Page, “Equationally complete varieties of generalized groups,” Bull. Austral. Math. Soc.,13, No. 1, 75–83 (1975).
P. M. Cohn, Universal Algebra, Harper and Row, New York-Evanston-London (1965).
G. Grätzer, Universal Algebra, Van Nostrand, Princeton (1968).
J. Smith, Mal'cev Varieties, Springer-Verlag, Berlin-Heidelberg-New York (1976).
B. Csákány, “Varieties of affine modules,” Acta Sci. Math.,37, Nos. 1-2, 3–10 (1975).
V. A. Artamonov, “Free n-groups,” Mat. Zametki,8, No. 4, 499–507 (1970).
G. Cupona, “On (m, n)-rings,” Bileten Drusht. Mat. Fiz. SRM, In Mathematical Reviews this journal is given as Bull. Soc. Math. Phys. Macedoine — Translator.16, 5–10 (1965).
J. D. Monk and F. M. Sioson, “On the general theory of m-groups,” Fund. Math.,72, No. 3, 233–244 (1971).
A. G. Kurosh, “Multioperator rings and algebras,” Usp. Mat. Nauk,24, No. 1, 3–15 (1969).
N. Bourbaki, Commutative Algebra, Addison-Wesley (1972).
V. A. Artamonov, “Latices of varieties of linear algebras,” Usp. Mat. Nauk,33, No. 2, 135–167 (1978).
V. K. Kharchenko, “Generalized identities involving automorphisms in associative rings with identity,” Algebra Logika,14, No. 6, 681–699 (1975).
C. Procesi, Rings with Polynomial Identities, Marcel-Dekker, New York (1973).
N. Jacobson, PI-Algebras. An Introduction, Springer-Verlag, Berlin-Heidelberg-New York (1975).
E. L. Post, “Polyadic groups,” Trans. Am. Math. Soc.,48, 208–350 (1940).
J. W. S. Cassels and A. Fröhlich (editors), algebraic Number Theory [Russian translation], Mir, Moscow (1969).
D. Gorenstein, Finite Groups, Harper and Row, New York (1968).
W. Feit and J. G. Thompson, “Solvability of groups of odd order,” Pac. J. Math.,13, No. 3, 775–1029 (1963).
V. M. Busarkin and Yu. M. Gorchakov, Finite Groups That Admit Partitions [in Russian], Nauka, Moscow (1968).
R. B. Warfield, Nilpotent Groups, Springer-Verlag, Berlin-Heidelberg-New York (1976).
D. M. Clark and P. H. Krauss, “Para-primal algebras,” Algebra Univers.,6, No. 2, 165–192 (1976).
Additional information
Moscow State University, Moscow. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 21, No. 3, pp. 6–22, May–June, 1980.
Rights and permissions
About this article
Cite this article
Artamonov, V.A. Minimal varieties of generalized semigroups, groups, and rings. Sib Math J 21, 319–332 (1980). https://doi.org/10.1007/BF00968175
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00968175