MV-semirings and their Sheaf Representations

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.