%0 Journal Article
%T On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
%A Jipsen, Peter
%A Ledda, Antonio
%A Paoli, Francesco
%J Reports on Mathematical Logic
%V 2013
%R 10.4467/20842589RM.13.001.1201
%N Number 48
%P 3-36

%@ 0137-2904
%D 2013
%U https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/on-some-properties-of-quasi-mv-algebras-and-quasi-mv-algebras-part-iv
%X 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].