TY - JOUR
TI - On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
AU - Jipsen, Peter
AU - Ledda, Antonio
AU - Paoli, Francesco
TI - On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV
AB - 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].
VL - 2013
IS - Number 48
PY - 2013
SN - 0137-2904
C1 - 2084-2589
SP - 3
EP - 36
DO - 10.4467/20842589RM.13.001.1201
UR - https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/on-some-properties-of-quasi-mv-algebras-and-quasi-mv-algebras-part-iv