On some Properties of quasi-MV √ Algebras and quasi-MV Algebras. Part IV

• Authors: Peter Jipsen , Antonio Ledda , Francesco Paoli
• Languages of publication: PL

Abstracts

PL

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].

Keywords

PL

• Publisher: [unknown2]
• Journal: Reports on Mathematical Logic
• Year: 2013
• Volume: 48

Dates

published

2013

online

07 - 07 - 2015

Contributors

author

Peter Jipsen

author

Antonio Ledda

author

Francesco Paoli