Let R be a commutative ring with identity and all modules are unital. Various generalizations
of primary ideals and primary modules have been studied. For example, a proper ideal I of R …

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 …

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 …

All rings are assumed to be associative and to have a nonzero identity element. Let A be a
ring, and let M be a right A-module. A proper ideal P of the ring A is said to be right primitive …

Let $ R $ be a commutative ring and let $ M $ be an $ R $-module. A submodule $ N $ of $
M $ is called a weakly primal submodule provided that the set $ P= w (N)\cup\{0\} $ forms an …

It is shown that if every prime ideal minimal over an ideal I is finitely generated, then there
are only finitely many prime left ideals minimal over I. This immedeately generalizes Cohen's …

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 …

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 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 …

Weakly prime ideals in a commutative ring with non-zero identity have been introduced and
studied in Anderson and Smith, Houston J. Math. 29: 831840, 2003. Here we study the …