Semigroups satisfying (xy)m = xmym

Thomas E Nordahl

doi:10.1007/BF02194776

Semigroups satisfying (xy)^m = x^my^m

Thomas E Nordahl

Psychiatry and Behavioral Sciences

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

In this paper we characterize Archimedean semigroups with idempotents satisfying (xy)^m = x^my^m as exactly those semigroups which are a retract extension of a completely simple semigroup satisfying (xy)^m = x^my^m by a nil semigroup satisfying (xy)^m = x^my^m. 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 language	English (US)
Pages (from-to)	332-346
Number of pages	15
Journal	Semigroup Forum
Volume	8
Issue number	1
DOIs	https://doi.org/10.1007/BF02194776
State	Published - Dec 1974

ASJC Scopus subject areas

Mathematics(all)

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AB - 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

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Semigroups satisfying (xy)^m = x^my^m

Abstract

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