CLASSICAL 2-ABSORBING SECONDARY SUBMODULES

‎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 $abNsubseteq K$‎, ‎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.