Almost Schreier monoids.
type: Item
instance of: scholarly article
title: Almost Schreier monoids.
zbMATH Open document ID: 1252.20058
author: Tiberiu Dumitrescu
author: Waseem Khalid
published in: Algebra Universalis
publication date: 2012-03-01T00:00:00Z
review text: The notion almost-Schreier monoid is introduced and investigated. Here, a monoid means a (multiplicative) commutative semigroup with \(1\) and \(0\), such that the semigroup without \(0\) is cancellative; an example to keep in mind is a domain when only multiplication is considered as operation. Indeed, earlier the authors considered almost-Schreier domains, and in the present paper generalize these investigations to a purely multiplicative setting. A monoid \(H\), in the above sense, is called an almost-Schreier monoid if for non-zero \(a,b_1,b_2\) in \(H\) with \(a\mid b_1b_2\) one has that there exists some integer \(k\) such that \(a^k=a_1a_2\) and \(a_1\mid b_1^k\) and \(a_2\mid b_2^k\). First, several characterizations of almost-Schreier monoids are obtained, and some of there basic properties established. Then, more detailed investigations are undertaken. For example, it is shown that the \(t\)-class group of an almost-Schreier monoid is a torsion group; and, that among \(t\)-Prüfer monoids, almost-Schreier monoids are characterized by this property.
Mathematics Subject Classification ID: 20M14
Mathematics Subject Classification ID: 13F05
zbMATH DE Number: 6010372
zbMATH Keywords: almost-Schreier monoids
zbMATH Keywords: class groups
zbMATH Keywords: Schreier domains
zbMATH Keywords: Prüfer monoids
zbMATH Keywords: discrete valuation monoids
zbMATH Keywords: t-ideals
zbMATH Keywords: commutative semigroups
reviewed by: Wolfgang A. Schmid
MaRDI profile type: Publication
full work available at URL: s00012-011-0164-x
OpenAlex ID: W2037962537
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DOI: 10.1007/S00012-011-0164-X
description: scientific article; zbMATH DE number 6010372