Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Weakly Classical Prime Submodules

  • Mostafanasab, Hojjat (Department of Mathematics and Applications, University of Mohaghegh Ardabili) ;
  • Tekir, Unsal (Department of Mathematics, Marmara University) ;
  • Oral, Kursat Hakan (Department of Mathematics, Yildiz Technical University, Davutpasa Campus)
  • Received : 2016.05.21
  • Accepted : 2016.09.01
  • Published : 2016.12.23
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Abstract

In this paper, 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 $m{\in}M$ and elements a, $b{\in}R$, $abm{\in}N$ implies that $am{\in}N$ or $bm{\in}N$. We introduce the concept of "weakly classical prime submodules" and we will show that this class of submodules enjoys many properties of weakly 2-absorbing ideals of commutative rings. A proper submodule N of M is a weakly classical prime submodule if whenever $a,b{\in}R$ and $m{\in}M$ with $0{\neq}abm{\in}N$, then $am{\in}N$ or $bm{\in}N$.

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