Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGS

  • Darani, Ahmad Yousefian (Department of Mathematics Faculty of Science University of Mohaghegh Ardabili) ;
  • Soheilnia, Fatemeh (Department of Mathematics Faculty of Science University of Mohaghegh Ardabili) ;
  • Tekir, Unsal (Department of Mathematics Marmara University) ;
  • Ulucak, Gulsen (Department of Mathematics Gebze Technical University)
  • Received : 2016.08.16
  • Accepted : 2017.03.07
  • Published : 2017.09.01
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Abstract

Assume that M is an R-module where R is a commutative ring. A proper submodule N of M is called a weakly 2-absorbing primary submodule of M if $0{\neq}abm{\in}N$ for any $a,b{\in}R$ and $m{\in}M$, then $ab{\in}(N:M)$ or $am{\in}M-rad(N)$ or $bm{\in}M-rad(N)$. In this paper, we extended the concept of weakly 2-absorbing primary ideals of commutative rings to weakly 2-absorbing primary submodules of modules. Among many results, we show that if N is a weakly 2-absorbing primary submodule of M and it satisfies certain condition $0{\neq}I_1I_2K{\subseteq}N$ for some ideals $I_1$, $I_2$ of R and submodule K of M, then $I_1I_2{\subseteq}(N:M)$ or $I_1K{\subseteq}M-rad(N)$ or $I_2K{\subseteq}M-rad(N)$.

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References

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