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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2019, Number 1, Pages 39–51
(Mi basm491)
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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.
Received: 26.05.2018
Citation:
Rafieh Razavi Nazari, Shaban Ghalandarzadeh, “On fully idempotent semimodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 1, 39–51
Linking options:
https://www.mathnet.ru/eng/basm491 https://www.mathnet.ru/eng/basm/y2019/i1/p39
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Abstract page: | 197 | Full-text PDF : | 90 | References: | 22 |
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