@article { author = {Farshadifar, F.}, title = {CLASSICAL 2-ABSORBING SECONDARY SUBMODULES}, journal = {Journal of Algebraic Systems}, volume = {8}, number = {1}, pages = {7-15}, year = {2020}, publisher = {Shahrood University of Technology}, issn = {2345-5128}, eissn = {2345-511X}, doi = {10.22044/jas.2019.7287.1359}, abstract = {‌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.}, keywords = {Secondary module,2-absorbing primary ideal,classical 2-absorbing secondary module}, url = {https://jas.shahroodut.ac.ir/article_1762.html}, eprint = {https://jas.shahroodut.ac.ir/article_1762_45c478c6d71b1cbd202a21bc668d31f3.pdf} }