Countably McCoy rings

Authors : Samir BOUCHİBA, Abderrazzak AİT OUAHİ, Youssef NAJEM

Pages : 725-736

Doi:10.15672/hujms.910906

View : 21 | Download : 7

Publication Date : 2022-06-01

Article Type : Research Paper

Abstract :The main goal of this paper is to study the class of countably $\mathcal {A}$-rings insert ignore into journalissuearticles values(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}$-rings insert ignore into journalissuearticles values(or McCoy rings); and the class of total-$\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