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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the structure of certain idempotent semigroups
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by Ahmad Shafaat PDF
Trans. Amer. Math. Soc. 149 (1970), 371-378 Request permission

Abstract:

Some general theorems concerning residual finiteness of algebras are given that are applied to show that every idempotent semigroup satisfying $xyzx = xzyx$ identically is a subcartesian product of certain simple semigroups of order two and three.
References
  • P. M. Cohn, Universal algebra, Harper & Row, Publishers, New York-London, 1965. MR 0175948
  • J. A. Gerhard and Ahmad Shafaat, Semivarieties of idempotent semigroups (prepublication copy).
  • J. R. Isbell, Subjects, adequacy, completeness and categories of algebras. [Subobjects, adequacy, completeness and categories of algebras], Rozprawy Mat. 36 (1964), 33. MR 163939
  • Miyuki Yamada and Naoki Kimura, Note on idempotent semigroups. II, Proc. Japan Acad. 34 (1958), 110–112. MR 98141
  • B. H. Neumann, Group properties of countable character (prepublication copy).
  • Ahmad Shafaat, On implicationally defined classes of algebras, J. London Math. Soc. 44 (1969), 137–140. MR 237409, DOI 10.1112/jlms/s1-44.1.137
  • —, Characterizations of some universal classes of algebras, J. London Math. Soc. (to appear).
  • Takayuki Tamura, Attainability of systems of identities on semigroups, J. Algebra 3 (1966), 261–276. MR 190255, DOI 10.1016/0021-8693(66)90001-9
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 149 (1970), 371-378
  • MSC: Primary 20.93
  • DOI: https://doi.org/10.1090/S0002-9947-1970-0258995-0
  • MathSciNet review: 0258995