On fully idempotent semimodules

Rafieh Razavi Nazari ; Shaban Ghalandarzadeh

Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2019), pp. 39-51.

Résumé

Let $S$ be a semiring and $M$ an $S$-semimodule. Let $N$ and $L$ be subsemimodules of $M$. Set $N\star L:=Ho{m}_S(M,L)N=\sum \{\phi (N)\mid \phi \in Ho{m}_S(M,L)\}$. 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.

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