Centralizers of full injective transformations in the symmetric inverse semigroup
type: Item
instance of: scholarly article
title: Centralizers of full injective transformations in the symmetric inverse semigroup
zbMATH Open document ID: 1435.20071
author: Janusz Konieczny
published in: Semigroup Forum
publication date: 2018-07-26T00:00:00Z
review text: The study of centralizers in group theory is a wide topic with enumerable connections. In semigroup theory, the topic has also been considered, in particular within transformation semigroups, for example by Araújo, Konieczny or Lipscomb. Here, contrary to what happens when dealing with permutations, different cases have required particular approaches, depending on being total or partial, injective or not,\dots. In this paper, the author considers total injective maps on a set $X$ within the symmetric inverse semigroup $I(X)$. For each Green relation $S$, the author describes the total injective maps $f$ for which the relation $S$ on its centralizer, the subsemigroup $C(f)$ of $I(X)$, is a restriction of the respective relation $S$ on $I(X)$. Such description is presented in terms of the cycle-ray decomposition of $f$, which generalizes the cycle decomposition of a permutation.
reviewed by: Gracinda M. S. Gomes
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M15
zbMATH DE Number: 6911208
zbMATH Keywords: centralizer
zbMATH Keywords: symmetric inverse semigroup
zbMATH Keywords: Green's relations
MaRDI profile type: Publication
full work available at URL: s00233-017-9884-3
OpenAlex ID: W2642982138
Wikidata QID: Q114230643
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DOI: 10.1007/S00233-017-9884-3
description: scientific article; zbMATH DE number 6911208