Semiannihilator small submodules with respect to an arbitrary submodule

TL;DR

This paper introduces a generalization of semiannihilator small submodules in module theory, extending the concept to T-semiannihilator small submodules relative to any submodule T of a module M over a commutative ring.

Contribution

The paper proposes the concept of T-semiannihilator small submodules, broadening the existing framework to include arbitrary submodules T, thus enhancing the theoretical understanding of submodule structures.

Findings

Defined T-semiannihilator small submodules

Extended properties of semiannihilator small submodules

Provided examples illustrating the new concept

Abstract

In this paper R will denote a commutative ring with identity and M a nonzero unital R-module. We will generalize the concept of semiannihilator small submodules to the T-semiannihilator small submodules with respect to an arbitrary submodule T of M.