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 …

The main goal of this paper is to study the class of countably A-rings (or the countably
McCoy rings) introduced by T. Lucas in [The diameter of a zero divisor graph, J. Algebra …

The purpose of this paper is to study the strong version of countably A-rings (or the
countably McCoy rings) introduced by T. Lucas in [21]. Moreover, we introduce and …

We study rings $ R $ for which whenever non-zero polynomials $ f (x) $ and $ g (x) $ satisfy
$ f (x) g (x) f (x)= 0$, it implies that there is a non-zero element $ r\in R $ such that $ f (x) rf …

We in this note consider a new concept, so called π-McCoy, which unifies McCoy rings and
IFP rings. The classes of McCoy rings and IFP rings do not contain full matrix rings and …

Based on McCoy's theorem on commutative rings, Nielsen called a ring R right McCoy if the
equation f (x) g (x)= 0 implies f (x) c= 0 for some nonzero element c in R, where f (x) and g (x) …

We introduce two subclasses of abelian McCoy rings, socalled π-CN-rings and π-duo rings,
and systematically study their fundamental characteristic properties accomplished with …

We introduce Central McCoy rings, which are a generalization of McCoy rings and
investigate their properties. For a ring R, we prove that R is right Central McCoy if and only if …

In this article, we give several generalizations of the concept of zero-divisor elements in a
commutative ring with identity to modules. Then, for each 𝑅-module 𝑀, we associate three …

Based on the well-known theorem of McCoy for polynomials and its generalization, by
Roitman [, Theorem 3.1], we introduce the concept of Mc-extension. An extension A⊆ B of …