فهرست نشریات علمی دسترسی آزاد ایران

Let $R$ be a commutative ring with identity $1\neq 0$ and $M$ a nonzero unital $R$-module. In this paper, we introduce a new notion of submodules in $M$, namely $T$-semi-annihilator small submodules of $M$ with respect to an arbitrary submodule $T$ of $M$. A submodule $N$ of $M$ is $T$-semi-annihilator small in $M$ provide that for each submodule $X$ of $M$ with $T\subseteq N+X$ implies that ${\rm Ann}(X)\ll (T:M)$.  In addition, we investigate some results concerning to this new class of submodules. Among various results, we prove that for a faithful finitely generated multiplication module $M$, the submodule $N$ of $M$ is a $T$-semi-annihilator small submodule of $M$ if and only if  $(N:M)$ is a $(T:M)$-semi-annihilator small ideal of $R$. Finally, we explore the properties and the behaviour of this structure under ring homomorphism, localization, direct sums and tensor product of them with a faithfully flat $R$-module.