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On Quotient Hypermodules

Volume 18, Number 1 (2015), 90 - 97

On Quotient Hypermodules

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Abstract

A hypermodule is a multivalued algebraic system satisfying the module like axioms. In this paper, we construct quotient hypermodule. Let $M$ be a hypermodule, $N$ be a subhypermodule of $M$ and $I$ be a hyperideal of $R$. Then, $[M:N^{\ast}]$ is $R$-hypermodule and $[R:I^{\ast}]$-hypermodule, and prove that when $N$ is normal subhypemodule, $[M:N^{\ast}]$ is a $[R:I^{\ast}]$-module. Hence, the quotient hypermodules considered by Anvarieh and Davvaz are modules.