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.