Direct products of cyclic semigroups and unions of groups
type: Item
instance of: scholarly article
title: Direct products of cyclic semigroups and unions of groups
zbMATH Open document ID: 0828.20048
DOI: 10.1007/BF02573518
author: D. C. Jackson
published in: Semigroup Forum
publication date: 1995-12-18T00:00:00Z
full work available at URL: https://eudml.org/doc/135380
review text: It is proved that if \(S\times\bigcup_{e\in E} G_e\) is isomorphic to \(T\times\bigcup_{f\in F} H_f\), where \(S\) and \(T\) are direct products of non-group finite cyclic semigroups, \(\bigcup_{e\in E} G_e\) and \(\bigcup_{f\in F} H_f\) are unions of finite groups with \(E\) and \(F\) finite sets of idempotents and \(G_e\), \(H_f\) groups for each \(e\in E\), \(f\in F\), then \(S\cong T\) and \(\bigcup_{e\in E} G_e\cong\bigcup_{f\in F} H_f\). Conditions under which a finite semigroup has such a decomposition are given. Then an algorithm for finding the direct factors is presented.
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 736955
zbMATH Keywords: direct decompositions
zbMATH Keywords: direct products
zbMATH Keywords: finite cyclic semigroups
zbMATH Keywords: unions of finite groups
zbMATH Keywords: idempotents
zbMATH Keywords: finite semigroups
zbMATH Keywords: algorithm
reviewed by: Jaromír Duda
MaRDI profile type: Publication
cites work: Finite direct products of finite cyclic semigroups and their characterization
cites work: The unique factorization problem for finite relational structures
cites work: Q5532570
cites work: Refinement properties for relational structures
cites work: Q3848243
OpenAlex ID: W2039594769
description: scientific article; zbMATH DE number 736955