TitleOn some varieties of MTL-Algebras
Publication TypeJournal Article
Year of Publication2005
AuthorsNoguera C, Esteva F, Gispert J
JournalLogic Journal of the IGPL. May 2005.
Volume13
Number4
Pagination443 - 466
Abstract

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i.e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras, 0, as those for which the quotient by the radical is a Boolean algebra. We prove that 0 is the variety generated by all perfect MTL-algebras and give some equational bases for it. We also introduce a new way to build MTL-algebras by adding a negation fixpoint to a perfect algebra and also by adding some set of points whose negation is the fixpoint. Finally, we consider the varieties generated by those algebras, giving equational bases for them, and we study which of them define a fuzzy logic with standard completeness theorem.