Related papers: Orthocomplete Pseudo MV-algebras
We study $\mathbb H$-perfect pseudo MV-algebras, that is, algebras which can be split into a system of ordered slices indexed by the elements of an subgroup $\mathbb H$ of the group of the real numbers. We show when they can be represented…
A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an interval in the lexicographic product of a linear unital group with an arbitrary $\ell$-group. We present conditions when a pseudo MV-algebra is lexicographic. We show…
The aim of the paper is to study epicomplete objects in the category of $MV$-algebras. A relation between injective $MV$-algebras and epicomplete $MV$-algebras is found, an equivalence condition for an $MV$-algebra to be epicomplete is…
The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions of a square root on a pseudo MV-algebra, and present their main properties. We show that the class of pseudo-MV-algebras with square roots is…
We study algebraic conditions when a pseudo MV-algebra is an interval in the lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras and…
We present a complete characterization of subdirectly irreducible MV-algebras with internal states (SMV-algebras). This allows us to classify subdirectly irreducible state morphism MV-algebras (SMMV-algebras) and describe single generators…
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, the main aim is to continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations.…
General theory determines the notion of separable MV-algebra (equivalently, of separable unital lattice-ordered Abelian group). We establish the following structure theorem: An MV-algebra is separable if, and only if, it is a finite product…
In this paper we propose a semiring-theoretic approach to MV-algebras based on the connection between such algebras and idempotent semirings - such an approach naturally imposing the introduction and study of a suitable corresponding class…
In \cite{DvZa3}, we started the investigation of pseudo MV-algebras with square roots. In the present paper, we continue to study the structure of pseudo MV-algebras with square roots focusing on their new characterizations. The paper is…
We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated…
We investigate the structure of perfect residuated lattices, focussing especially on perfect pseudo MV-algebras. We show that perfect pseudo MV-algebras can be represented as a generalised version of kites of Dvure\v{c}enskij and Kowalski,…
The paper deals with an algebraic extension of $MV$-algebras based on the definition of generalized Boolean algebras. We introduce a new algebraic structure, not necessarily with a top element, which is called an $EMV$-algebra and every…
We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as…
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…
Complete MV-algebras are naturally equipped with frame structures. We call them MV-frames and investigate some of their main the properties as frames. We completely characterized algebraic MV-frames as well as regular MV-frames. In…
In this article, we introduce mock-Lie superalgebras, we give some definitions, properties, constructions, and we study their representations. Moreover we introduce pseudo-euclidean mock-Lie superalgebras which are mock-Lie superalgebras…
The main aim of this article is to study tense MV-algebras which are just MV-algebras with new unary operations $G$ and $H$ which express a universal time quantifiers. Tense MV-algebras were introduced by D. Diagonescu and G. Georgescu.…
In this paper, we generalize Schur-Weyl duality and Morita Theorem on associative algebras to those on associative $H$-pseudoalgebras. Meanwhile, we get a plenty of associative $H$-pseudoalgebras over a cocommutative Hopf algebra $H$.
We connect the dual adjunction between MV-algebras and Tychonoff spaces with the general theory of natural dualities, and provide a number of applications. In doing so, we simplify the aforementioned construction by observing that there is…