On graded Jgr-2-absorbing primary submodule

Abstract

This paper introduces the concept of graded J_gr-2-absorbing primary submodules, a new intermediate structure in graded module theory. Motivated by the need to extend and unify classical notions such as graded prime and graded primary submodules, the study develops a comprehensive framework describing their defining characteristics and relationships. Through a sequence of rigorous theorems and illustrative examples, we establish fundamental properties, equivalence conditions, and inclusion relations that clarify the behavior of these submodules within graded modules. The findings show that graded J_gr-2-absorbing primary submodules generalize several known structures while maintaining distinctive algebraic flexibility.  Moreover, the results concerning graded homomorphisms and multiplication modules demonstrate the robustness of the concept and its potential applications in graded algebra.  Overall, this work deepens the theoretical understanding of graded algebraic systems and provides a foundation for further research in module and ring theory.