Spectrum of prime L-submodules

Authors:
R. Ameri;R. Mahjoob
Affiliations:
Department of Mathematics, Faculty of Basic Science, University of Mazandaran, Babolsar, Iran;Department of Mathematics, Faculty of Basic Science, University of Mazandaran, Babolsar, Iran
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

Let L be a complete lattice. We introduce and characterize the prime L-submodules of a unitary module over a commutative ring with identity. Finally, we investigate the Zariski topology on the prime L-Spectrum of a unitary module, consisting of the collection of all prime L-submodules, and prove that for L-top modules the Zariski topology on L-Spec(M) exists.