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Transactions of the American Mathematical Society

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On the structure of certain idempotent semigroups


Author: Ahmad Shafaat
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
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Abstract | References | Similar Articles | Additional Information

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

  • [1] P. M. Cohn, Universal algebra, Harper and Row, New York, 1965. MR 31 #224. MR 0175948 (31:224)
  • [2] J. A. Gerhard and Ahmad Shafaat, Semivarieties of idempotent semigroups (prepublication copy).
  • [3] J. R. Isbell, Subobjects, adequacy, completeness and categories of algebras, Rozprawy Mat. 36 (1964). MR 29 #1238. MR 0163939 (29:1238)
  • [4] Naoki Kimura, Note on idempotent semigroups. II, Proc. Japan. Acad. 34 (1958), 110-112. MR 0098141 (20:4603)
  • [5] B. H. Neumann, Group properties of countable character (prepublication copy).
  • [6] Ahmad Shafaat, Implicationally defined classes of algebras, J. London Math. Soc. 44 (1969), 137-140. MR 38 #5691. MR 0237409 (38:5691)
  • [7] -, Characterizations of some universal classes of algebras, J. London Math. Soc. (to appear).
  • [8] T. Tamura, Attainability of systems of identities on semigroups, J. Algebra 3 (1966), 261-276. MR 32 #7668. MR 0190255 (32:7668)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1970-0258995-0
Keywords: Infinitely long implications, implicationally defined classes of $ \Omega $-algebras, quasivarieties, semivarieties, residually finite and locally finite algebras, classes of countable (local) character, idempotent semigroups, normal idempotent semigroups
Article copyright: © Copyright 1970 American Mathematical Society

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