On Graded 2-Absorbing Coprimary Submodules

Abstract

The aim of this article is to introduce the concept of graded 2absorbing coprimary submodules as a generalization of graded strongly 2-absorbing second submodules, and explore some properties of this class. A non-zero graded R-submodule N of a graded R-module M is called a graded 2-absorbing coprimary R-submodule if whenever x, y are homogeneous elements of R and K is a graded R-submodule of M such that xyN ⊆ K, then either x or y is in the graded radical of (K : R N ) or xy ∈ Ann R (N ). Several results have been achieved.