The main purpose of this paper is to introduce and investigate a new class of rings lying
properly between the class of 𝒜-rings and the class of 𝒮 𝒜-rings. The new class of rings …

We present an answer to a problem raised by Anderson and Chun in [DD Anderson and S.
Chun, Annihilator conditions on modules over commutative rings, J. Algebra Appl. 16 …

In this paper we show that if {Ri} i∈ I is a family of commutative rings and {Mi} i∈ I is a family
of modules such that each Mi is an Ri-module, then the direct product Mi is a-module over Ri …

The main purpose of this paper is to generalize a result of TG Lucas which states that if R is
a reduced commutative ring and M is a flat R-module, then the idealization R⋉ M is an A …

In this paper, we introduce and investigate a new class of modules that is closely related to
the class of Noetherian modules. Let $ R $ be a commutative ring and $ M $ be an $ R …

Let R be a commutative ring and M be an R-module. A submodule N of M is called a d-
submodule ( resp., an fd-submodule ) if \ann_R(m)⊆\ann_R(m') ( resp …

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 …

Let R be a commutative ring with 1≠ 0 and M a unital R-module. M is said to satisfy Property
(A) if for each finitely generated ideal J of R contained in ZR (M), there exists 0≠ m∈ M such …

A+ B rings are constructed from a ring A and nonempty set of prime ideals of A. Initially,
these rings were created to provide examples of reduced rings which satisfy certain …

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 …