Geodesic
Spectra of semimodules
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 15-28

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The purpose of this paper is to investigate possible structures and useful properties of prime subsemimodules of a semimodule $M$ over a semiring $R$ and show various applications of the properties. The main part of this work is to introduce a new class of semimodules over $R$ called strong primeful $R$-semimodules. It is shown that every non-zero strong primeful semimodule possesses the non-empty prime spectrum with the surjective natural map. Also, it is proved that this class contains the family of finitely generated $R$-semimodules properly. 
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     author = {Reza Ebrahimi Atani and Shahabaddin Ebrahimi Atani},
     title = {Spectra of semimodules},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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Reza Ebrahimi Atani; Shahabaddin Ebrahimi Atani. Spectra of semimodules. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2011), pp. 15-28. http://geodesic.mathdoc.fr/item/BASM_2011_3_a1/