The aim of this paper is to introduce the notion of nearly prime submodules as a
generalization of prime submodules. We investigate some of their basic properties and point …

WEAKLY PRIME SUBMODULES AND PRIME SUBMODULES Page 1 Glasgow Math. J. 48 (2006)
343–346. C 2006 Glasgow Mathematical Journal Trust. doi:10.1017/S0017089506003119 …

This paper presents two generalizations, one of prime submodules called S (N)− locally
prime submodules and the other of weakly prime submodules called S (N)− weakly prime …

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 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 …

A proper submodule N of a module M over a ring R is said to be prime (or P-prime) if re e N
for re R and ee M implies that either ee N or re P= N: M. In other words, N is a prime …

In this paper we investigate-primary submodules which unify prime submodules and primary
submodules. Our motivation is to extend the concept of-primary ideals into-primary …

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let (M) be
the set of all submodules of M, and φ:(M)→(M)∪{∅} be a function. We say that a proper …

This paper aims to introduce a new class of submodules, called (m, n)-semiprime
submodule, which is a generalization of semiprime submodule. Let M be a unital A-module …

Let R be a commutative ring with identity. For an R-module M, the notion of strongly prime
submodule of M is defined. It is shown that this notion of prime submodule inherits most of …