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Transactions of the American Mathematical Society

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



On the structure of certain idempotent semigroups

Author: Ahmad Shafaat
Journal: Trans. Amer. Math. Soc. 149 (1970), 371-378
MSC: Primary 20.93
MathSciNet review: 0258995
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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.

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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