The aim of this paper is to study unitary regular modules on commutative rings with identity.
Regularity accompanied by cocyclic property results in some prime-related conclusions on …

We investigate prime submodules of regular modules. In particular, we shall see that every
proper submodule of a regular module M over an integral domain is prime. Although (von …

In this paper, we investigate the class of von Neumann regular modules over commutative
rings. More precisely, we introduce a characterization of regular modules, and then, we …

Different and distinct notions of regularity for modules exist in the literature. When these
notions are restricted to commutative rings, they all coincide with the well-known von …

Let R be a commutative ring with nonzero identity. Our objective is to investigate
representable modules and to examine in particular when submodules of such modules are …

The notion of $ R $-regular module is introduced. We will show that if $ M $ is a torsion-free
module over a commutative ring, then $ M $ is $ R $-regular module if and only if $ M $ is a …

Let $ R $ be a commutative ring with non-zero identity. We define a proper submodule $ N $
of an $ R $-module $ M $ to be weakly prime if $0\not= rm\in N $($ r\in R, m\in M $) implies …

ON REGULARITY OF RINGS 1 Page 1 ON REGULARITY OF RINGS 1 Jianlong Chen Department
of Mathematics, Harbin Institute of Technology Harbin 150001, PR China and Department of …

Let R be a commutative ring with non-zero identity. We define a proper submodule N of an R-
module M to be weakly prime if 0≠ rm∈ N (r∈ R, m∈ M) implies m∈ N or rM⊆ N. A …

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 …