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 classical 2-absorbing secondary submodule of M if whenever a; b ∈ R, K is a submodule of M and abN ⊆ K, then aN ⊆ K or bN ⊆ K or ab ∈ √ AnnR(N). This can be regarded as a dual notion of the 2-absorbing primary submodule.