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On some properties of quasi-MV algebras and square root ' quasi-MV algebras

Paoli F., Ledda A., Freytes H.

Reports on Mathematical Logic

2009

Vol. 44

31-63

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV alge- bras and square root ' 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 square root ' quasi- MV algebras; we give a representation of semisimple square root ' quasi-MV algebras in terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties.