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On some properties of quasi MV algebras and square root quasi MV algebras. Part III

100%

Paoli F. , Kowalski T.

Reports on Mathematical Logic

2010

tom Vol. 45

161-199

In the present paper, which is a sequel to [14] and [3], we investigate further the structure theory of quasi-MV algebras and square root' quasi-MV algebras. In particular: we provide an improved version of the subdirect representation theorem for both varieties; we characterise the Ursini ideals of quasi-MV algebras; we establish a restricted version of J�Lonsson�fs lemma, again for both varieties; we simplify the proof of standard completeness for the variety of square root ' quasi-MV algebras; we show that this same va- riety has the finite embeddability property; finally, we investigate the structure of the lattice of subvarieties of Square root' quasi-MV algebras.

On some properties of quasi-MV algebras and √' quasi-MV algebras. Part IV

80%

Jipsen P. , Ledda A. , Paoli F.

Reports on Mathematical Logic

2013

tom Vol. 48

3--36

In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasi- MV algebras and √' quasi-MV algebras. In particular: we pro- vide a new representation of arbitrary√' MV algebras in terms of √'MV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √' MV varieties, proving that it is uncountable, providing equational bases for some of its members, as well as analysing a number of slices of special interest; we show that the variety of √'MV algebras has the amalgamation property; we provide an axiomatisation of the 1-assertional logic of √'MV algebras; lastly, we reconsider the correspondence between Carte- sian √'MV algebras and a category of Abelian lattice-ordered groups with operators first addressed in [10].

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

80%

Paoli F. , Ledda A. , Freytes H.

tom 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.