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Related papers: A duality for (n+1)-valued MV-algebras

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An alternative proof of bornological Verdier duality for complex manifolds, as proven initially by Prosmans & Schneiders is given, using Schneider's theory of quasi-abelian homological algebra, and the theory of residues and duality.

Complex Variables · Mathematics 2023-08-08 Christopher Burns

We develop dualities for complete perfect distributive quasi relation algebras and complete perfect distributive involutive FL-algebras. The duals are partially ordered frames with additional structure. These frames are analogous to the…

Logic in Computer Science · Computer Science 2026-01-30 Andrew Craig , Peter Jipsen , Claudette Robinson

We show that for quasivarieties of p-algebras the properties of (i) having decidable first-order theory and (ii) having decidable first-order theory of the finite members, coincide. The only two quasivarieties with these properties are the…

Logic · Mathematics 2024-09-16 Tomasz Kowalski , Katarzyna Słomczyńska

In this paper, once recalled some properties of CMV-algebras, we introduce an expansion of the one-variable fragment of Lukasiewicz propositional logic whose algebraic semantics is the variety of CMV-algebras.

Logic · Mathematics 2011-09-21 Antonio Di Nola , Brunella Gerla , Ciro Russo

The abstract notion of Tamarkin-Tsygan calculus with duality gives Batalin- Vilkovisky structures in a general setting. We apply this technique to the case of Van den Bergh duality for algebras to prove that Calabi-Yau algebras are…

K-Theory and Homology · Mathematics 2009-07-24 Thierry Lambre

We study the category of graded representations with finite--dimensional graded pieces for the current algebra associated to a simple Lie algebra. This category has many similarities with the category $\cal O$ of modules for $\lie g$ and in…

Representation Theory · Mathematics 2012-07-11 Matthew Bennett , Arkady Berenstein , Vyjayanthi Chari , Anton Khoroshkin , Sergey Loktev

We extend Priestley Duality to suitable categories of fuzzy topological spaces and ordered algebraic structures that generalize bounded distributive lattices. The duality we prove extends not only classical Priestley Duality between…

Category Theory · Mathematics 2026-04-17 Marby Zuley Bolaños Ortiz , Ciro Russo

MV-monoids are algebras $\langle A,\vee,\wedge, \oplus,\odot, 0,1\rangle$ where $\langle A, \vee, \wedge, 0, 1\rangle$ is a bounded distributive lattice, both $\langle A, \oplus, 0 \rangle$ and $\langle A, \odot, 1\rangle$ are commutative…

Rings and Algebras · Mathematics 2025-04-11 Marco Abbadini , Paolo Aglianò , Stefano Fioravanti

Here we initiate an investigation into the class mLMn{\times}m of monadic n{\times}m-valued Lukasiewicz-Moisil algebras (or mLMn{\times}m-algebras), namely n{\times}m-valued Lukasiewicz-Moisil algebras endowed with a unary operation called…

Logic · Mathematics 2014-04-10 Aldo V. Figallo , Claudia Sanza

We present a Stone duality for bitopological spaces in analogy to the duality between Stone spaces and Boolean algebras, in the same vein as the duality between d-sober bitopological spaces and spatial d-frames established by Jung and…

General Topology · Mathematics 2026-01-27 Hang Yang , Dexue Zhang

We use category theory to propose a unified approach to the Schur-Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras…

Representation Theory · Mathematics 2011-05-13 Alexei Davydov , Alexander Molev

We introduce a theory of volume polynomials and corresponding duality algebras of multi-fans. Any complete simplicial multi-fan $\Delta$ determines a volume polynomial $V_\Delta$ whose values are the volumes of multi-polytopes based on…

Combinatorics · Mathematics 2016-12-12 Anton Ayzenberg , Mikiya Masuda

Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…

Logic · Mathematics 2025-10-28 Xiaohao Liu , Heyan Wang , Wenjuan Chen

In this paper, we investigate related properties of some particular derivations and give some characterizations of additive derivations in MV-algebras. Then, we obtain that the fixed point set of additive derivations is still an MV-algebra.…

Logic · Mathematics 2017-09-18 Jun Tao Wang , Bijan Davvaz , Peng Fei He

We propose in this article a definition of a MV-algebra structure on a class of subsets of some probability spaces and we work-out some examples. Our intention is to convey, by mean of the simplest possible examples, the idea that the…

Logic · Mathematics 2016-05-05 Gianluca Caterina , Vittorio Cafagna

The present study shows how to enrich De Morgan algebras with a perfection operator that allows one to express the Boolean properties of negation-consistency and negation-determinedness. The variety of perfect paradefinite algebras thus…

Logic · Mathematics 2022-04-11 Joel Gomes , Vitor Greati , Sérgio Marcelino , João Marcos , Umberto Rivieccio

Plonka sums consist of an algebraic construction similar, in some sense to direct limits, which allows to represent classes of algebras defined by means of regular identities (namely those equations where the same set of variables appears…

Logic · Mathematics 2020-04-20 Stefano Bonzio

It has been known since the work of Duskin and Pelletier four decades ago that KH^op, the category opposite to compact Hausdorff spaces and continuous maps, is monadic over the category of sets. It follows that KH^op is equivalent to a…

Logic · Mathematics 2020-11-19 Vincenzo Marra , Luca Reggio

The authors developed in a recent paper natural dualities for finitely generated quasivarieties of Sugihara algebras. They thereby identified the admissibility algebras for these quasivarieties which, via the Test Spaces Method devised by…

Rings and Algebras · Mathematics 2019-03-12 L. M. Cabrer , H. A. Priestley

Our main issue was to understand the connection between \L ukasiewicz logic with product and the Pierce-Birkhoff conjecture, and to express it in a mathematical way. To do this we define the class of \textit{f}MV-algebras, which are…

Logic · Mathematics 2016-05-05 Serafina Lapenta , Ioana Leustean