Identities of the natural representation of the infinitely based semigroup
HTML articles powered by AMS MathViewer
- by Leonid Al’shanskii and Alexander Kushkuley PDF
- Proc. Amer. Math. Soc. 118 (1993), 931-937 Request permission
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
- Peter Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1969), 298–314. MR 233911, DOI 10.1016/0021-8693(69)90058-1 B. I. Plotkin, Varietes of representations of groups, Uspekhi Mat. Nauk. 32 (1977), 3-68. (Russian)
- 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
- P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
- Nathan Jacobson, $\textrm {PI}$-algebras, Lecture Notes in Mathematics, Vol. 441, Springer-Verlag, Berlin-New York, 1975. An introduction. MR 0369421, DOI 10.1007/BFb0070021 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)
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 118 (1993), 931-937
- MSC: Primary 20M07; Secondary 08B05
- DOI: https://doi.org/10.1090/S0002-9939-1993-1132406-6
- MathSciNet review: 1132406