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## On fully idempotent semimodules

Authors: R. Razavi Nazari, S. Ghalandarzadeh

### Abstract

Let $S$ be a semiring and $M$ an $S$-semimodule. Let $N$ and $L$ be subsemimodules of $M$. Set $N\star L:= Hom_{S}(M,L)N=\sum\{\varphi(N)\mid \varphi\in Hom_{S}(M,L)\}$. Then $N$ is called an idempotent subsemimodule of $M$, if $N=N\star N$. An $S$-semimodule $M$ is called fully idempotent if every subsemimodule of $M$ is idempotent. In this paper we study the concept of fully idempotent semimodules as a generalization of fully idempotent modules and investigate some properties of idempotent subsemimodules of multiplication semimodules.

Faculty of Mathematics
K.N. Toosi University of Technology
Tehran, Iran
E-mail: ,

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