In this article, we introduce the dual notions of strongly prime, weakly prime, semiprime, and
primal submodules, that is, strongly second, weakly second, semisecond, and secondal …

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 …

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 …

All rings are commutative with 1= 0, and all modules are unital. The purpose of this paper is
to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing …

Let R be a ring, M be a left R-module and Spec (RM) be the collection of all prime
submodules of M. In this paper and its sequel, we introduce and study a generalization of …

We introduce the notion of classical primary submodules that generalizes the concept of
primary ideals of commutative rings to modules. Existence and uniqueness of classical …

A proper submodule N of an R-module M is called a weakly prime [resp. a prime]
submodule, if for any elements a, b∈ R and x∈ M, the condition abx∈ N [resp. ax∈ N] …

Let M be a left R-module. A proper submodule P of M is called classical prime if for all ideals
and for all submodules N⊆ M, implies that or. We generalize the Baer–McCoy radical (or …

Let M be a left R-module. Then a proper submodule P of M is called weakly prime
submodule if for any ideals A and B of R and any submodule N of M such that ABN⊆ P, we …

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 …