Geodesic
On subsemimodules of semimodules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 20-30 Cet article a éte moissonné depuis la source Math-Net.Ru

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P. J. Allen [1] introduced the notion of a $Q$-ideal and a construction process was presented by which one can build the quotient structure of a semiring modulo a $Q$-ideal. Here we introduce the notion of $Q_M$-subsemimodule $N$ of a semimodule $M$ over a semiring $R$ and construct the factor semimodule $M/N$. It is shown that this notion inherits most of the essential properties of the factor modules over a ring. 
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Reza Ebrahim Atani; Shahabaddin Ebrahimi Atani. On subsemimodules of semimodules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2010), pp. 20-30. http://geodesic.mathdoc.fr/item/BASM_2010_2_a1/

[1] Allen P. J., “A fundamental theorem of homomorphisms for simirings”, Proc. Amer. Math. Soc, 21 (1969), 412–416 | DOI | MR | Zbl

[2] Ebrahimi Atani S., “The ideal theory in quotients of commutative semirings”, Glasnik Matematicki, 42 (2007), 301–308 | DOI | MR | Zbl

[3] Ebrahimi Atani R., Ebrahimi Atani S., “Ideal theory in commutative semirings”, Buletinul Acad. Sci. Rep. Moldova ser. Math., 2008, no. 2(57), 14–23 | MR | Zbl

[4] Golan J. S., The theory of semirings with applications in mathematics and theoretical computer Science, Pitman Monographs and Surveys in Pure and Applied Mathematics, Longman Scientific and Technical, 1992 | MR | Zbl

[5] Hebisch U., Weinert U. J., Halbringe – Algebraische Theorie und Anwendungen in der Informatik, Teubner, Stuttgart, 1993 | MR | Zbl

[6] Lu C. P., “Prime submodules of modules”, Comment. Univ. St. Pauli, 33 (1984), 61–69 | MR | Zbl

[7] Maze G., Monico C., Rosenthal J., Public key cryptography on semigroup actions, 28 Jan. 2005, arXiv: cs.CR/0501017v2 | MR