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IMCS/Publications/BASM/Issues/BASM n.3 (67), 2011/

Spectra of semimodules

Authors: Reza Ebrahimi Atani, Shahabaddin Ebrahimi Atani

Abstract

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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