On fully idempotent semimodules

Rafieh Razavi Nazari, Shaban Ghalandarzadeh

Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

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.

Keywords and phrases: semiring, fully idempotent semimodule, multiplication semimodule, regular semimodule.

MSC: 16Y60

Received: 26.05.2018

Language: English