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

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 provide a new representation of arbitrary √ ′qMV algebras in terms of √ ′qMV algebras arising out of their MV* term subreducts of regular elements; we investigate in greater detail the structure of the lattice of √ ′qMV 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 √ ′qMV algebras has the amalgamation property; we provide an axiomatisation of the 1-assertional logic of √ ′qMV algebras; lastly, we reconsider the correspondence between Cartesian √ ′qMV algebras and a category of Abelian lattice-ordered groups with operators first addressed in [10].