Proceedings of the American Mathematical Society

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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
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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.


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  • [1] M. V. Volkov and M. V. Sapir, HFB property and structure of semigroups, Contributions to general algebra, 6, Hölder-Pichler-Tempsky, Vienna, 1988, pp. 303–310. MR 1078051
  • [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. Mashevitskiĭ, Example of a finite semigroup that does not have an irreducible basis of identities in the class of completely 0-simple semigroups, Uspekhi Mat. Nauk 38 (1983), no. 2(230), 211–212 (Russian). MR 695480
  • [4] A. H. Clifford and G. B. Preston, The algebraic theory of semigroups. Vol. I, Mathematical Surveys, No. 7, American Mathematical Society, Providence, R.I., 1961. MR 0132791
  • [5] L. N. Shevrin and M. V. Volkov, Identities of semigroups, Izv. Vyssh. Uchebn. Zaved. Mat. 11 (1985), 3–47, 85 (Russian). MR 829099
  • [6] M. V. Sapir, Problems of Burnside type and the finite basis property in varieties of semigroups, Izv. Akad. Nauk SSSR Ser. Mat. 51 (1987), no. 2, 319–340, 447 (Russian); English transl., Math. USSR-Izv. 30 (1988), no. 2, 295–314. MR 897000
  • [7] T. K. Braun, Locally finite semigroups, Ukrain. Mat. Ž. 20 (1968), 732–738 (Russian). MR 0237683
  • [8] Charles F. Fennemore, All varieties of bands. I, II, Math. Nachr. 48 (1971), 237–252; ibid. 48 (1971), 253-262. MR 0294535

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DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1185274-1
Article copyright: © Copyright 1994 American Mathematical Society