On Classical Weakly Prime Submodules

Abstract

The aim of this paper is to introduce the concept of classical weakly prime submodules which is the generalization of the notion of weakly classical prime submodules to modules over arbitrary noncommutative rings. We study some properties of classical weakly prime submodules and investigate their structure in different classes of modules. Also, the structure of such submodules of modules over duo rings is completely described. We investigate some properties of classical weakly prime submodules of multiplication modules.

Intuitionistic L-fuzzy classical prime and intuitionistic L-fuzzy 2-absorbing submodules

“…We recall that a proper submodule N of M is called a prime submodule of M if, for every a ∈ R and m ∈ M , am ∈ N implies that either m ∈ N or a ∈ (N : R M ). The notion of prime submodules was first introduced and studied in [11] and recently it has received a good deal of attention from several authors [7,14]. Clearly every prime submodule is classical prime submodule and every classical prime submodule is 2-absorbing submodule.…”