Some Properties of Quasi - Mv Algebras

A b s t r a c t. We investigate some properties of two varieties of algebras arising from quantum computation quasi-MV algebras and √ ′ quasi-MV algebras first introduced in [13], [12] and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of √ ′ quasiMV algebras; we give a representation of semisimple √ ′ quasi-MV algebras in terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties.