Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the joins of semigroup varieties with the variety of commutative semigroups

Authors: M. V. Sapir and M. V. Volkov
Journal: Proc. Amer. Math. Soc. 120 (1994), 345-348
MSC: Primary 20M07
MathSciNet review: 1185274
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that the join of a variety of semigroups and the variety of all commutative semigroups is not finitely based, provided some weak conditions.

References [Enhancements On Off] (What's this?)

  • [1] M. V. Volkov and M. V. Sapir, $ HFB$ property and structure of semigroups, Contrib. Gen. Algebra, vol. 6, 1988, pp. 303-310. MR 1078051 (92e:20046)
  • [2] T. Nordahl, On the join of the variety of all bands and the variety of all commutative semigroups via conditional rewrite rules, Proceedings of the International Colloquium on Words, Semigroups and Combinatorics, Kioto, 1990.
  • [3] G. I. Mashevitskii, An example of a finite semigroup without irreducible identity basis in the class of completely 0-simple semigroups, Uspekhi Mat. Nauk 38 (1983), 211-213. (Russian) MR 695480 (85a:20027)
  • [4] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups, vol. 1, Amer. Math. Soc., Providence, RI, 1961. MR 0132791 (24:A2627)
  • [5] L. N. Shevrin and M. V. Volkov, Identities of semigroups, Izv. Vyssh. Uchebn. Zaved. Mat. 1985, no. 11, 3-47. (Russian) MR 829099 (87f:20094)
  • [6] M. V. Sapir, Burnside type problems and finite basis property in semigroup varieties, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), 319-340. (Russian) MR 897000 (88h:20078)
  • [7] T. C. Brown, On locally finite semigroups, Ukrain. Mat. Zh. 20 (1968), 732-738. (Russian) MR 0237683 (38:5964)
  • [8] C. F. Fennemore, All varieties of bands, Math. Nachr. 48 (1971), 237-262. MR 0294535 (45:3605)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20M07

Retrieve articles in all journals with MSC: 20M07

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society