A class of finite rings having one-sided zero divisors
type: Item
instance of: scholarly article
title: A class of finite rings having one-sided zero divisors
zbMATH Open document ID: 0734.16006
author: Zimei Jiang
published in: Chinese Science Bulletin
publication date: 1991-01-01T00:00:00Z
review text: Let R be a ring, let \(S_ 0\) and \(\Sigma\) denote the set of right zero divisors which are not left zero divisors and left identities which are not right identities, respectively. The author proves that if R is a finite ring then the following statements are equivalent: (i) \(S_ 0\neq 0\), \(R=\cup_{e\in \Sigma}eRe \cup eR(1-e),\) (ii) There exists a ring M such that R is isomorphic to a minimal right ideal A of M, and moreover, A has no identity and \(A^ 2\neq 0\).
Mathematics Subject Classification ID: 16P10
zbMATH DE Number: 4214216
zbMATH Keywords: right zero divisors
zbMATH Keywords: left identities
zbMATH Keywords: finite ring
zbMATH Keywords: minimal right ideal
reviewed by: Kwangil Koh
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4214216