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.
Equivalences between subcategories of MTL-algebras via Boolean algebras and prelinear semihoops / S. Aguzzoli, T. Flaminio, S. Ugolini. - In: JOURNAL OF LOGIC AND COMPUTATION. - ISSN 0955-792X. - 27:8(2017), pp. 2525-2549.
Equivalences between subcategories of MTL-algebras via Boolean algebras and prelinear semihoops
S. Aguzzoli
;
2017
Abstract
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.File | Dimensione | Formato | |
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