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 …

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 all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a {\it classical primary submodule}, if for each …

As a proper generalization of the modules with the properties (E) and (EE) that were
introduced by Zoschinger in terms of supplements, we say that a module M has the property …

Let R be a commutative ring and M an R-module. Let Z (M)={r∈ R| rm= 0 for some nonzero
m∈ M} and T (M)={m∈ M| rm= 0 for some nonzero r∈ R}. M satisfies Property A …

It is of obvious interest to know whether an algebraic property of modules is preserved by
direct sums of such modules. In this paper we provide a survey of this question for various …

A commutative ring R has Property (A) if every finitely generated ideal of R consisting
entirely of zero-divisors has a nonzero annihilator. We continue in this paper the study of …

The purpose of this paper is to further the study of weakly injective and weakly projective
modules as a generalization of injective and projective modules. For a locally qfd module …

In this article, we introduce the notion of strongly 𝜋-regular module which is a generalization
of von Neumann regular module in the sense [13]. Let 𝐴 be a commutative ring with 1≠ 0 …

In this paper, we study modules with the properties (CRE) and (CREE), which are adapted
Zöschinger's modules with the properties. E/and. EE/. It is shown that:(1) a module M has the …