Countably McCoy rings
Authors : Samir Bouchiba, Abderrazzak Ait Ouahi, Youssef Najem
Pages : 725-736
Doi:10.15672/hujms.910906
View : 11 | Download : 4
Publication Date : 2022-06-01
Article Type : Research
Abstract :The main goal of this paper is to study the class of countably $\mathcal {A}$-rings (or the countably McCoy rings) introduced by T. Lucas in [The diameter of a zero divisor graph, J. Algebra 301 , 174-193, 2006] which turns out to lie properly between the class of $ \mathcal{A}$-rings (or McCoy rings) and the class of total-$\mathcal{A}$-rings. Also, we introduce and investigate the module theoretic version of the countably $\mathcal {A}$-ring notion, namely the countably $\mathcal {A}$-modules. Our focus is shed on the behavior of the countably $\mathcal {A}$-property vis-à-vis the polynomial ring, the power series ring, the idealization and the direct products. Numerous examples are provided to show the limits of the results.Keywords : countably McCoy rings, countably McCoy modules, Noetherian ring, $mathcal{A}$-ring, $mathcal{A}$-module, zero divisor