Weakly classical 1-absorbing primary submodules

Abstract

In this paper, we introduce weakly classical 1-absorbing primary submodules of an unital module over a commutative ring with nonzero identity. Consider H as a module over a ring D. A proper submodule E of H is called weakly classical 1-absorbing primary submodule, if for each nonunit alpha,beta,gamma is an element of D and mu is an element of H with 0 not equal alpha beta gamma mu is an element of E, it follows that either alpha beta mu is an element of E or gamma(t)mu is an element of E for some t >= 1. Various properties and characterizations of weakly classical 1-absorbing primary submodules are explored.