Semigroups satisfying (xy)m = xmym

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Abstract

In this paper we characterize Archimedean semigroups with idempotents satisfying (xy)m = xmym as exactly those semigroups which are a retract extension of a completely simple semigroup satisfying (xy)m = xmym by a nil semigroup satisfying (xy)m = xmym. Regular semigroups satisfying (xy)2 = x2y2 are exactly those semigroups which are a spined product of a band and a semigroup which is a semilattice of Abelian groups. A semigroup which is a nil extension of a regular semigroup satisfies (xy)2 = x2y2 if and only if it is a retract extension of a regular semigroup satisfying (xy)2 = x2y2 by a nil semigroup satisfying (xy)2 = x2y2

Original languageEnglish (US)
Pages (from-to)332-346
Number of pages15
JournalSemigroup Forum
Volume8
Issue number1
DOIs
Publication statusPublished - Dec 1974

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ASJC Scopus subject areas

  • Mathematics(all)

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