Let R be a commutative ring with unity and let B be a submodule of a non-zero left R-module
D, B is called semiprime if whenever aky∈ B, a∈ R, y∈ D, k∈ Z+ implies ay∈ B. We say …

Let R be a commutative ring with identity and M be an R-module. As a new generalization of
primary ideals to modules, a proper submodule N of M is a primary-like submodule if …

In this paper we continue our study about quasi-primary submodules (probably satisfying the
primeful property), that was defined and studied in Part I (see [8]). We define a quasi-primary …

Let R be a commutative ring with identity and let M be a unitary R-module. A submodule N of
M is said to be a multiple of M if N= rM for some r 𝜖 R. If every submodule of M is a multiple …

In this note, we will make an intensive study of the notion of primal submodules of a module
over a commutative ring with identity. First, a number of results concerning of primal …

It is known that every semiprime ring is a subdirect sum of prime rings. This is a
consequence of the fact that every semiprime ideal is an intersection of prime ideals. We aim …

Let R be a commutative ring with identity and M be a unitary R-module. Let ϕ: S (M)→ S
(M)∪{∅} be a function, where S (M) is the set of submodules of M. Suppose n≥ 2 is a …

Comaximal Submodules of Multiplication Modules 1 Introduction Page 1 International
Mathematical Forum, 5, 2010, no. 24, 1179 - 1183 Comaximal Submodules of Multiplication …

We have introduced the notion of $\alpha $-prime and weakly $\alpha $-prime submodules
as a generalization of prime submodules. Some basic properties of $\alpha $-prime and …

Let R be a commutative ring with identity and M a unitary R-module. The concept of PRIME
SUBMODULE of an R-module M has been discussed. In this paper, we investigate the …