On seminormal semigroups
type: Item
instance of: scholarly article
title: On seminormal semigroups
zbMATH Open document ID: 0898.20043
author: Mitsuo Kanemitsu
author: Ryûki Matsuda
published in: Archiv der Mathematik
publication date: 1998-11-03T00:00:00Z
review text: This paper studies the semigroup analogs of results about seminormal overrings from [Commun. Algebra 10, 1421-1448 (1982; Zbl 0496.13001)]\ by \textit{D. Dobbs, J. Huckaba}, and the reviewer. A (nonzero) commutative, torsion-free cancellative semigroup \(S\) with 0, written additively and with quotient \(G\), is said to be seminormal if whenever \(2a,3a\in S\) for \(a\in G\), then \(a\in S\). Two of the main results for one-dimensional semigroups are (1) if \(S\) is seminormal, then each integral oversemigroup of \(S\) is seminormal, and (2) each oversemigroup of \(S\) is seminormal if and only if both \(S\) is seminormal and its integral closure \(S'\) is a valuation semigroup.
Mathematics Subject Classification ID: 20M14
zbMATH DE Number: 1145424
zbMATH Keywords: seminormal semigroups
zbMATH Keywords: commutative torsion-free cancellative semigroups
zbMATH Keywords: one-dimensional semigroups
zbMATH Keywords: integral oversemigroups
zbMATH Keywords: integral closures
zbMATH Keywords: valuation semigroups
reviewed by: David F. Anderson
MaRDI profile type: Publication
full work available at URL: s000130050122
OpenAlex ID: W2046473184
DOI: 10.1007/S000130050122
description: scientific article; zbMATH DE number 1145424