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, $S\subseteq R$ 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.