TY - JOUR ID - 1762 TI - CLASSICAL 2-ABSORBING SECONDARY SUBMODULES JO - Journal of Algebraic Systems JA - JAS LA - en SN - 2345-5128 AU - Farshadifar, F. AD - Department of Mathematics, Farhangian University, Tehran, Iran. Y1 - 2020 PY - 2020 VL - 8 IS - 1 SP - 7 EP - 15 KW - Secondary module KW - 2-absorbing primary ideal KW - classical 2-absorbing secondary module DO - 10.22044/jas.2019.7287.1359 N2 - ‌In this work‌, ‌we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‌. ‌Let $R$ be a commutative ring with‌‌identity‌. ‌We say that a non-zero submodule $N$ of an $R$-module $M$ is a‌‌\emph{classical 2-absorbing secondary submodule} of $M$ if whenever $a‌, ‌b \in R$‌, ‌$K$ is a submodule of $M$ and $abN\subseteq K$‌,‌then $aN \subseteq K$ or $bN \subseteq K$ or $ab \in \sqrt{Ann_R(N)}$‌.‌This can be regarded as a dual notion of the 2-absorbing primary submodule‌. UR - https://jas.shahroodut.ac.ir/article_1762.html L1 - https://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdf ER -