On ϕ-2-Absorbing Primary Submodules

• Published in: Acta mathematica vietnamica Vol. 42; no. 1; pp. 27 - 35
• Main Authors: Moradi, Razieh, Ebrahimpour, Mahdieh
• Format: Journal Article
• Language: English
• Published: Singapore Springer Singapore 01.03.2017; Springer Nature B.V
• Subjects: Mathematics; Mathematics and Statistics; Modules; 2-absorbing submodules; Primary submodules; 13C13; Weakly 2-absorbing primary submodules; 13C05; 2-absorbing primary submodules
• ISSN: 0251-4184; 2315-4144
• DOI: 10.1007/s40306-016-0181-0

Let R be a commutative ring with identity and M be a unitary R -module. Let ϕ : S ( M ) → S ( M ) ∪ { ∅ } 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 x ∈ N ∖ ϕ ( N ) implies r x ∈ N , or s x ∈ N , or rs ∈ ( N : M ) , where r , s ∈ R and x ∈ M . 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.