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Proceedings of the Edinburgh Mathematical Society (1)

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1 results

Answers to Some Questions Concerning Rings with Property (A)
Part of
- Rings and algebras arising under various constructions
E. Hashemi, A. AS. Estaji, M. Ziembowski
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 60 / Issue 3 / August 2017

Published online by Cambridge University Press:

31 January 2017, pp. 651-664
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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.