Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 27–35

# On ϕ-2-Absorbing Primary Submodules

• Mahdieh Ebrahimpour
Article

## Abstract

Let R be a commutative ring with identity and M be a unitary R-module. Let $$\phi :S(M)\rightarrow S(M)\cup \{\emptyset \}$$ be a function, where S(M) is the set of submodules of M. We say that a proper submodule N of M is a ϕ-2-absorbing primary submodule if r s xNϕ(N) implies r xN, or s xN, or $$rs\in \sqrt {(N:M)}$$, where r,sR and xM. In this paper, we study ϕ-2-absorbing primary submodules and we prove some basic properties of these submodules. Also, we give a characterization of ϕ-2-absorbing primary submodules and we investigate ϕ-2-absorbing primary submodules of some well-known modules.

## Keywords

Primary submodules ϕ-2-absorbing primary submodules Weakly 2-absorbing primary submodules ϕ-2-absorbing submodules 2-absorbing submodules

13C05 13C13

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