On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
Peter Jipsen, Antonio Ledda, Francesco Paoli · UNICA IRIS Institutional Research Information System (University of Cagliari) · 2013
In the present paper, which is a sequel to [20, 4, 12], we investigate further the structure theory of quasiMV algebras and √0quasi-MV algebras. In particular: we provide a new representation of arbitrary √0qMV algebras in terms of √0qMV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √0qMV 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 √0qMV algebras has the amalgamation property; we provide an axiomatisation of the 1-assertional logic of √0qMV algebras; lastly, we reconsider the correspondence between Cartesian √0qMV algebras and a category of Abelian lattice-ordered groups with operators first addressed in [10].