# Small submodules with respect to an arbitrary submodule

Document Type: Research Paper

Authors

Lorestan University

Abstract

Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $T\subseteq X+N$ implies that $T\subseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

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