On 2-Absorbing Primary Submodules of Modules over Commutative Rings

Abstract

In this article, 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 ∈ M and elements a, b ∈ R, abm ∈ N implies that am ∈ N or bm ∈ N . We introduce the concept of "classical 2-absorbing submodules" as a generalization of "classical prime submodules". We say that a proper submodule N of M is a classical 2-absorbing submodule if whenever a, b, c ∈ R and m ∈ M with abcm ∈ N , then abm ∈ N or acm ∈ N or bcm ∈ N .

On Graded 2-Absorbing Primary and Graded Weakly 2-Absorbing Primary Ideals

“…In [11], the concept of 2-absorbing primary ideal of a ring was extended to the notion of 2-absorbing primary submodule of a module. Let R be a ring and M be an R-module.…”

On classical n-absorbing submodules

“…The class of 2-absorbing submodules of modules was introduced as a generalization of the class of 2-absorbing ideals of rings. Then, many generalizations of 2-absorbing submodules were studied such as primary 2-absorbing [8], almost 2-absorbing [3], almost 2-absorbing primary [2], and classical 2-absorbing [9]. In this article, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules.…”

On 2-absorbing quasi primary submodules

“…One of the main interest of many researchers is to generalize the notion of prime submodule by using different ways. For instance, 2-absorbing submodule which is a generalization of prime submodules was firstly introduced and studied in [9], after that another generalization, which is called 2-absorbing primary submodule was studied in [15].…”