Document Type: Original Manuscript

Author

Department of Mathematics, Farhangian University, Tehran, Iran.

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 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.

Keywords