M-zeroids: structure and categorical equivalence
type: Item
instance of: scholarly article
title: M-zeroids: structure and categorical equivalence
zbMATH Open document ID: 1277.03069
author: Joshua B. Palmatier
author: F. Guzmán
published in: Studia Logica
publication date: 2013-01-03T00:00:00Z
review text: Since \textit{C. C. Chang} [Trans. Am. Math. Soc. 88, 467--490 (1958; Zbl 0084.00704)] first defined the algebraic systems called MV-algebras, numerous generalizations for MV-algebras have been proposed, including the structures called m-zeroids. In this paper the authors develop a method for constructing finite totally-ordered m-zeroids. They also prove that there is a categorical equivalence between the category of pseudo Łukasiewicz-like implicators and the category of finite totally-ordered m-zeroids.
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 6121540
zbMATH Keywords: finite totally-ordered m-zeroid
zbMATH Keywords: categorical equivalence
zbMATH Keywords: pseudo Łukasiewicz-like implicator
reviewed by: Dimitru Buşneag
MaRDI profile type: Publication
full work available at URL: s11225-012-9444-5
OpenAlex ID: W2073836169
cites work: Algebraic Analysis of Many Valued Logics
cites work: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
cites work: Q4836218
cites work: FUZZY LOGICAL OPERATORS ON FINITE CHAINS
cites work: A common abstraction of MV-algebras and abelian \(l\)-groups
DOI: 10.1007/S11225-012-9444-5
Recommended article: Q3062401
Recommended article: Q4253925
Recommended article: Q4786538
Recommended article: On the structure of zero morphisms in a quasi-pointed category
Recommended article: Q3726097
Recommended article: Q4951510
Recommended article: Q3091709
Recommended article: Equivalences of monoidal model categories
Recommended article: Categorical equivalences and realization theorems
Recommended article: Idempotent residuated structures: Some category equivalences and their applications
description: scientific article; zbMATH DE number 6121540