The duals of annihilator conditions for modules

TL;DR

This paper explores dual properties of submodules in modules over commutative rings, introducing new dual conditions and analyzing their structural implications.

Contribution

It introduces and investigates dual versions of Property A, strong Property A, and proper strong Property A for submodules, along with new properties SJ and IM J.

Findings

Characterization of dual Property A and its variants

Introduction of properties SJ and IM J for submodules

Structural insights into dual submodule conditions

Abstract

Let R be a commutative ring with identity and let M be an R-module. The purpose of this paper is to introduce and investigate the submodules of an R-module M which satisfy the dual of Property A, the dual of strong Property A, and the dual of proper strong Property A. Moreover, a submodule N of M which satisfy Property SJ (N) and Property IM J (N) will be introduced and investigated.