We say that an R-module M satisfies epi-ACC on submodules if in every ascending chain of
submodules of M, except probably a finite number, each module in chain is a homomorphic …

In this article, we study the notion of closed Rickart modules. A right R-module M is said to
be closed Rickart if, for each, is a closed submodule of M. Closed Rickart modules is a …

A proper submodule N of an R-module M is called a weakly prime [resp. a prime]
submodule, if for any elements a, b∈ R and x∈ M, the condition abx∈ N [resp. ax∈ N] …

On Unions of Prime Submodules Page 1 Southeast Asian Bulletin of Mathematics (2004) 28:
213-218 Southeast Asian Bulletin of Mathematics © SEAMS, 2004 On Unions of Prime …

In this paper we provide various properties of Rad-⊕-supplemented modules. In particular,
we prove that a projective module M is Rad-⊕-supplemented if and only if M is⊕ …

In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime, and
primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

An R-module M has Artinian prime factors if $ M/PM $ is an Artinian module for each prime
ideal P of R. For commutative rings R it is shown that Noetherian modules with Artinian …

Let G be a group, R be a ring and A be an RG-module. We say that A is an Artinian-finitary
module over RG if for every element g∈ G, the factor-module A/CA (g) is an Artinian R …

Inspired by the interplay between the Zariski topology defined on the prime spectrum of a
commutative ring R and the ring theoretic properties of R in [3, 8, 18, 23, 25], we introduce in …

Using the concepts of prime module, semiprime module and the concept of ascending chain
condition (ACC) on annihilators for an R-module M, we prove that if M is semiprime and …