Range sets and partition sets in connection with congruences and algebraic invariants
type: Item
instance of: scholarly article
title: Range sets and partition sets in connection with congruences and algebraic invariants
zbMATH Open document ID: 0783.20036
DOI: 10.1007/BF02573765
author: Inessa Levi
author: Steven Seif
published in: Semigroup Forum
publication date: 1994-04-05T00:00:00Z
full work available at URL: https://eudml.org/doc/135278
review text: Let \(S\) be a semigroup of transformations on a set \(X\). The authors define relations closed under inclusion on \(R(X)\), the set of ranges of mappings from \(S\). A new notion of connectedness for semigroups of transformations, called range-connectedness, is introduced. It is shown that equivalences closed under inclusion on \(R(X)\) and left-zero congruences on \(S\) are dually isomorphic iff \(S\) is range-connected. Further the relationship between right-zero congruences on \(S\) and equivalences closed under inclusion on the partition sets of \(S\) is studied. Partition-connected and partition-\(n\)-connected semigroups are introduced. These notions can be used to investigate an arbitrary semigroup \(S\) by considering faithful representations of \(S\) by semigroups of transformations.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 438886
zbMATH Keywords: semigroups of transformations
zbMATH Keywords: range-connectedness
zbMATH Keywords: equivalences closed under inclusion
zbMATH Keywords: congruences
zbMATH Keywords: right-zero congruences
zbMATH Keywords: partition sets
zbMATH Keywords: partition-\(n\)-connected semigroups
zbMATH Keywords: faithful representations
reviewed by: Jaromír Duda
MaRDI profile type: Publication
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OpenAlex ID: W2070917875
description: scientific article; zbMATH DE number 438886