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)



Identities of the natural representation of the infinitely based semigroup

Authors: Leonid Al’shanskii and Alexander Kushkuley
Journal: Proc. Amer. Math. Soc. 118 (1993), 931-937
MSC: Primary 20M07; Secondary 08B05
MathSciNet review: 1132406
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: An equational theory of a very small semigroup may fail to be finitely presented. A well-known example of such a semigroup was studied in detail by Peter Perkins some twenty years ago. We prove that the natural representation of his semigroup has a finite basis of identical relations and discuss this fact in a general context of universal algebra.

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

  • [1] Peter Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1969), 298–314. MR 0233911,
  • [2] B. I. Plotkin, Varietes of representations of groups, Uspekhi Mat. Nauk. 32 (1977), 3-68. (Russian)
  • [3] Yu. P. Razmyslov, Varieties of representations of finite-dimensional algebras in prime algebras, Vestnik Moskov. Univ. Ser. I Mat. Mekh. 6 (1982), 31–37, 120 (Russian, with English summary). MR 685260
  • [4] P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
  • [5] Nathan Jacobson, 𝑃𝐼-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin-New York, 1975. An introduction. MR 0369421
  • [6] A. N. Trahtman, A base of identities of the five-element semigroup of Brandt, Research in Modern Algebra, Sverdlovsk Univ., Sverdlovsk, 1987, pp. 147-149. (Russian)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20M07, 08B05

Retrieve articles in all journals with MSC: 20M07, 08B05

Additional Information

Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society