Equivalences between subcategories of MTL-algebras via Boolean algebras and prelinear semihoops

Stefano Aguzzoli, Tommaso Flaminio, Sara Ugolini

This article studies the class of strongly perfect MTL-algebras, i.e. MTL-algebras having an involutive co-radical, and the variety they generate, namely SBP0. Once these structures will be introduced, we will first establish categorical equivalences for several of their relevant proper subvarieties by employing a generalized notion of triplets whose main components are a Boolean algebra and a prelinear semihoop. When triplets are further expanded by a suitable operation between their semihoop reducts, we define a category of quadruples that are equivalent to the whole category of SBP0-algebras. Finally, we will provide an explicit representation of SBP0-algebras in terms of (weak) Boolean products.

Keywords: Strongly perfect MTL-algebras, Boolean Algebras, Prelinear Semihoops, Categorical Equivalence

Journal of Logic and Computation, exx014, https://doi.org/10.1093/logcom/exx014