MV-semirings and their Sheaf Representations |
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Authors: | Lawrence Peter Belluce Antonio Di Nola Anna Rita Ferraioli |
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Affiliation: | 1. Department of Mathematics, British Columbia University, Vancouver, British Columbia, Canada 2. Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo, 84084, Fisciano, Salerno, Italy
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Abstract: | In this paper we show that the classes of MV-algebras and MV-semirings are isomorphic as categories. This approach allows one to keep the inspiration and use new tools from semiring theory to analyze the class of MV-algebras. We present a representation of MV-semirings by MV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of MV-semirings over prime ideals. Using the categorical equivalence, we obtain a representation of MV-algebras. |
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