## Reports on Mathematical Logic

### No. 44

Francesco PAOLI, Antonio LEDDA, Roberto GIUNTINI, Hector FREYTES

On some properties of quasi-MV algebras and $\sqrt{^{\prime }}$ 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 $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} 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 $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties.