THE LOOMIS–SIKORSKI THEOREM FOR -ALGEBRAS

Abstract

An EMV-algebra resembles an MV-algebra in which a top element is not guaranteed. For$\unicode[STIX]{x1D70E}$-complete$EMV$-algebras, we prove an analogue of the Loomis–Sikorski theorem showing that every$\unicode[STIX]{x1D70E}$-complete$EMV$-algebra is a$\unicode[STIX]{x1D70E}$-homomorphic image of an$EMV$-tribe of fuzzy sets where all algebraic operations are defined by points. To prove it, some topological properties of the state-morphism space and the space of maximal ideals are established.