CLASSICAL 2-ABSORBING SECONDARY SUBMODULES | ||
| Journal of Algebraic Systems | ||
| مقاله 2، دوره 8، شماره 1، آذر 2020، صفحه 7-15 اصل مقاله (144.11 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2019.7287.1359 | ||
| نویسنده | ||
| F. Farshadifar* | ||
| Department of Mathematics, Farhangian University, Tehran, Iran. | ||
| چکیده | ||
| 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 with identity. 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. | ||
| کلیدواژهها | ||
| Secondary module؛ 2-absorbing primary ideal؛ classical 2-absorbing secondary module | ||
| مراجع | ||
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