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 …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …

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 …

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

Let R be a commutative ring with identity and M a unitary R-module, and n> 1 an integer
number. As a generalization of the concept of prime submodules, a proper submodule N of …

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 …

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 …

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 …

Let R be a commutative ring with non-zero identity. We define a proper submodule Nof an R-
module M to be quasi-primary if PM Nrad R=):(is a prime ideal of R. In this case we also say …