The main goal of this paper is to introduce and study the notion of Property (A) of a ring R or
an R-module M with respect to an ideal I of R. The new notion turns out to be a weak form of …

This paper introduces and studies the notion of Property ($\mathcal A $) of a ring $ R $ or an
$ R $-module $ M $ along an ideal $ I $ of $ R $. For instance, any module $ M $ over $ R …

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 …

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 …

Let R be a ring with unity, and let M be an unitary R-module. In this work we present strongly
pure ideal (sub module) concept as a generalization of pure ideal (sub module). Also we …

Let R be a ring with identity and M a unital right R-module. Let Z*(M)={m epsilon M: mR<< E
(mR)}. In this study we consider the property (T): For every right R-module M with Z*(M) …

Let R be a ring with an identity. A right R-module is said to be R-projective if every
homomorphism from M to R/I can be lifted to a homomorphism from M to R, for each right …

In 2005, M. Behboodi introduced the notion of a classical prime ring module, which he
showed is, in general, nonequivalent to a (Dauns) prime ring module. In this paper, we …

In this paper, we develop a systematic theory for the ideals of an L-ring L (μ, R). We
introduce the concepts of prime ideal, semiprime ideal, primary ideal and radical of an ideal …

In this paper, we introduce a strong property (A) as follows: A ring R is called satisfying
strong property (A) if every finitely generated ideal of R which is generated by a finite …