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Acta Mathematica Vietnamica

, Volume 42, Issue 1, pp 27–35 | Cite as

On ϕ-2-Absorbing Primary Submodules

  • Razieh Moradi
  • Mahdieh EbrahimpourEmail author
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 

Mathematics Subject Classification (2010)

13C05 13C13 

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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesVali-e-Asr UniversityRafsanjanIran

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