Varieties of MV-monoids and positive MV-algebras
Marco Abbadini, Paolo Aglian\`o, Stefano Fioravanti

TL;DR
This paper explores the structure and classification of MV-monoids and positive MV-algebras, providing axiomatizations and characterizations of their subvarieties, including minimal and finite irreducible cases.
Contribution
It offers a comprehensive analysis of the subvariety lattices of MV-monoids and positive MV-algebras, including axiomatizations and characterizations of key subclasses.
Findings
Characterized all almost minimal varieties of MV-monoids.
Identified and described finite subdirectly irreducible positive MV-algebras.
Axiomatized all varieties of positive MV-algebras.
Abstract
MV-monoids are algebras where is a bounded distributive lattice, both and are commutative monoids, and some further connecting axioms are satisfied. Every MV-algebra in the signature is term equivalent to an algebra that has an MV-monoid as a reduct, by defining, as standard, , , and . Particular examples of MV-monoids are positive MV-algebras, i.e. the -subreducts of MV-algebras. Positive MV-algebras form a peculiar quasivariety in the sense that, albeit having a logical motivation (being the quasivariety of subreducts of MV-algebras), it is not the…
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Taxonomy
TopicsAdvanced Algebra and Logic · Fuzzy and Soft Set Theory · Rough Sets and Fuzzy Logic
