Semigroups satisfying variable identities. II
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- by Mohan S. Putcha and Julian Weissglass
- Trans. Amer. Math. Soc. 168 (1972), 113-119
- DOI: https://doi.org/10.1090/S0002-9947-1972-0297902-3
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Abstract:
The concept of a semigroup satisfying an identity $xy = f(x,y)$ is generalized by considering identities in $n$-variables and letting the identity depend on the variables. The property of satisfying a “variable identity” is studied. Semigroups satisfying certain types of identities are characterized in terms of unions and semilattices of groups.References
- 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
- Mohan S. Putcha and Julian Weissglass, Semigroups satisfying variable identities, Semigroup Forum 3 (1971/72), no. 1, 64–67. MR 289693, DOI 10.1007/BF02572943
- Mohan S. Putcha and Julian Weissglass, A semilattice decomposition into semigroups having at most one idempotent, Pacific J. Math. 39 (1971), 225–228. MR 304523, DOI 10.2140/pjm.1971.39.225
- Takayuki Tamura, Semigroups satisfying identity $xy=f(x,\,y)$, Pacific J. Math. 31 (1969), 513–521. MR 260908, DOI 10.2140/pjm.1969.31.513 E. J. Tully, Semigroups satisfying an identity of the form $xy = {y^m}{x^n}$ (to appear).
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 168 (1972), 113-119
- MSC: Primary 20M05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0297902-3
- MathSciNet review: 0297902