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Keywords:
semi $n$-ideal; $n$-ideal; $n$-submodule; semi $n$-submodule
semi $n$-ideal; $n$-ideal; $n$-submodule; semi $n$-submodule
Summary:
Let $R$ be a commutative ring with identity and $M$ a unitary $R$-module. The purpose of this paper is to introduce the concept of semi-$n$-submodules as an extension of semi $n$-ideals and $n$-submodules. A proper submodule $N$ of $M$ is called a semi $n$-submodule if whenever $r\in R$, $m\in M$ with $r^{2}m\in N$, $r\notin \sqrt {0}$ and ${\rm Ann}_{R}(m)=0$, then $rm\in N$. Several properties, characterizations of this class of submodules with many supporting examples are presented. Furthermore, semi $n$-submodules of amalgamated modules are investigated.
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