Epimorphisms, permutation identities and finite semigroups
type: Item
instance of: scholarly article
title: Epimorphisms, permutation identities and finite semigroups
zbMATH Open document ID: 0546.20051
DOI: 10.1007/BF02573318
published in: Semigroup Forum
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134675
review text: In a joint result with N. M. Khan the author proves that a semigroup variety that admits the identity \(x_ 1x_ 2...x_ n=x_{1\pi}x_{2\pi}...x_{n\pi},\) where \(\pi\) is a permutation on 1,2,...,n is closed under taking epimorphisms iff either 1\(\pi \neq 1\) or \(n\pi \neq n\). A semigroup U is said to be saturated if the dominion of U in S is \(\neq S\) for every properly containing semigroup S. The author proves that any finite permutative semigroup is saturated.
Mathematics Subject Classification ID: 20M07
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 3869614
zbMATH Keywords: saturated semigroup
zbMATH Keywords: semigroup variety
zbMATH Keywords: epimorphisms
zbMATH Keywords: dominion
zbMATH Keywords: finite permutative semigroup
author: Peter M. Higgins
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3869614