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Answers to Some Questions Concerning Rings with Property (A)

Part of: Rings and algebras arising under various constructions

Published online by Cambridge University Press:  31 January 2017

E. Hashemi ,
A. AS. Estaji  and
M. Ziembowski
E. Hashemi
Affiliation:
Department of Mathematics, University of Shahrood, Shahrood, PO Box 316-3619995161, Iran ([email protected]; [email protected])
A. AS. Estaji
Affiliation:
Department of Mathematics, University of Shahrood, Shahrood, PO Box 316-3619995161, Iran ([email protected]; [email protected])
M. Ziembowski
Affiliation:
Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-662 Warsaw, Poland ([email protected])
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Abstract

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.

Keywords

rings with property (A)unique product monoidszip ringsreversible ringsMcCoy ringspolynomial rings

MSC classification

Secondary: 16S36: Ordinary and skew polynomial rings and semigroup rings 16S15: Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 60 , Issue 3 , August 2017 , pp. 651 - 664
Copyright
Copyright © Edinburgh Mathematical Society 2017 

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