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http://dx.doi.org/10.4134/JKMS.j160544

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)
Publication Information
Journal of the Korean Mathematical Society / v.54, no.5, 2017 , pp. 1505-1519 More about this Journal
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 $I_2K{\subseteq}M-rad(N)$.
Keywords
2-absorbing submodule; 2-absorbing primary submodule; weakly 2-absorbing primary submodule;
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Times Cited By KSCI : 2  (Citation Analysis)
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