Answers to Some Questions Concerning Rings with Property (A)

A ring R has right property (A) whenever a finitely generated two-sided ideal of R consisting entirely of left zero-divisors has a non-zero right annihilator. As the main result of this paper we give answers to two questions related to property (A), raised by Hong et al. One of the questions has a p...

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Bibliographic Details
Published inProceedings of the Edinburgh Mathematical Society Vol. 60; no. 3; pp. 651 - 664
Main Authors Hashemi, E., Estaji, A. AS, Ziembowski, M.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2017
Subjects
Log cabins
zip rings
polynomial rings
McCoy rings
reversible rings
unique product monoids
Primary 16S36
16S15
rings with property (A)
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Summary:A ring R has right property (A) whenever a finitely generated two-sided ideal of R consisting entirely of left zero-divisors has a non-zero right annihilator. As the main result of this paper we give answers to two questions related to property (A), raised by Hong et al. One of the questions has a positive answer and we obtain it as a simple conclusion of the fact that if R is a right duo ring and M is a u.p.-monoid (unique product monoid), then R is right M-McCoy and the monoid ring R[M] has right property (A). The second question has a negative answer and we demonstrate this by constructing a suitable example.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0013-0915
1464-3839
DOI:10.1017/S0013091516000407