Let R be a commutative ring and let M be an R-module. In this paper, we study the dual
notion of prime submodules (that is, second submodules of M). Also we introduce the dual …

The aim of this paper is to introduce the concept of classical weakly prime submodules
which is the generalization of the notion of weakly classical prime submodules to modules …

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N
of an R-module M to be (m, n)-closed if for r∈ R and b∈ M, r^{m} b∈ N implies rⁿ∈(N: _ {R} …

Most of the research on weakly prime and weakly 2-absorbing modules is for modules over
commutative rings. Only scatterd results about these notions with regard to non-commutative …

In this paper we extend from ideals to modules over commutative rings some results of
Fuchs, Heinzer and Olberding ([8],[9]) concerning primal and completely irreducible ideals …

In this article, we define almost prime submodules as a new generalization of prime and
weakly prime submodules of unitary modules over a commutative ring with identity. We …

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 …

Let R be an arbitrary ring and M be a right R-module. A proper submodule N of M is called
almost prime (respectively, weakly prime) if for each submodule K of M and each ideal I of R …

Modules over strongly prime rings Page 1 Journal of Algebra and Its Applications Vol. 14, No. 5
(2015) 1550076 (9 pages) c© World Scientific Publishing Company DOI: 10.1142/S0219498815500760 …

Let R be a commutative ring and m, n be positive integers. We define a proper submodule N
of an R-module M to be (m, n)-closed if for r∈ R and b∈ M, r^{m} b∈ N implies rⁿ∈(N: _ {R} …