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

16 Citations (Scopus)

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

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Semigroup

Regular Semigroup

Nil

Retract

Completely Simple Semigroup

Semilattice

Idempotent

Abelian group

If and only if

ASJC Scopus subject areas

Mathematics(all)

Cite this

Nordahl, T. E. (1974). Semigroups satisfying (xy)^m = x^my^m Semigroup Forum, 8(1), 332-346. https://doi.org/10.1007/BF02194776

Semigroups satisfying (xy)^m = x^my^m . / Nordahl, Thomas E.

In: Semigroup Forum, Vol. 8, No. 1, 12.1974, p. 332-346.

Research output: Contribution to journal › Article

Nordahl, TE 1974, 'Semigroups satisfying (xy)^m = x^my^m ', Semigroup Forum, vol. 8, no. 1, pp. 332-346. https://doi.org/10.1007/BF02194776

Nordahl TE. Semigroups satisfying (xy)^m = x^my^m Semigroup Forum. 1974 Dec;8(1):332-346. https://doi.org/10.1007/BF02194776

Nordahl, Thomas E. / Semigroups satisfying (xy)^m = x^my^m In: Semigroup Forum. 1974 ; Vol. 8, No. 1. pp. 332-346.

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10.1007/BF02194776