Some Properties of S-Semiannihilator Small Submodules and S-Small Submodules with respect to a Submodule

Abstract

Let R be a commutative ring with nonzero identity, S⊆R be a multiplicatively closed subset of R, and M be a unital R-module. In this article, we introduce the concepts of S-semiannihilator small submodules and S-T-small submodules as generalizations of S-small submodules. We investigate some basic properties of them and give some characterizations of such submodules, especially for (finitely generated faithful) multiplication modules.