Identities of regular semigroup rings
type: Item
instance of: scholarly article
title: Identities of regular semigroup rings
zbMATH Open document ID: 0907.20055
DOI: 10.1007/PL00005978
author: Haixuan Yang
published in: Semigroup Forum
publication date: 1999-03-07T00:00:00Z
review text: The problem ``which semigroup rings are rings with identity'' was raised a long time ago. In [Semigroup Forum 46, No. 1, 27-31 (1993; Zbl 0787.16024)], in order to investigate the existence of identity of an orthodox semigroup ring, \textit{F. Li} asked: for a ring \(R\) with identity and a regular semigroup \(S\), if \(RS\) is a ring with identity, is \(R\langle E(S)\rangle\) a ring with identity? The aim of this paper is to discuss this problem for FIC-semigroups and completely regular semigroups. The author proves that for an FIC-semigroup or a completely regular semigroup \(S\), if \(RS\) is a ring with identity, then \(R\langle E(S)\rangle\) is a ring with identity. \(E(S)\) denotes the set of idempotents of \(S\).
reviewed by: Fang Li
Mathematics Subject Classification ID: 20M25
Mathematics Subject Classification ID: 16S35
Mathematics Subject Classification ID: 20M17
zbMATH DE Number: 1209925
zbMATH Keywords: semigroup rings
zbMATH Keywords: existence of identity
zbMATH Keywords: FIC-semigroups
zbMATH Keywords: completely regular semigroups
zbMATH Keywords: idempotents
MaRDI profile type: Publication
full work available at URL: pl00005978
OpenAlex ID: W2024454786
description: scientific article; zbMATH DE number 1209925