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 ofMV-semirings byMV-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.

MV-semirings and their Sheaf Representations

DI NOLA, Antonio;FERRAIOLI, ANNA RITA
2013

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 ofMV-semirings byMV-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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/3986458
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