Related papers: Prime Filters in MV-algebras II
In this document we consider the prime spectrum of an MV-algebra with certain natural operations. These are used to show connections between the classes of prime lattice filters and prime implication filters.
In this document we consider a way of localizing an MV-algebra. Given any prime filter $F$ we find a local MV-algebra which has the same poset of prime filters as the poset of prime filters comparable to $F$.
In the last decade, interest in projective MV-algebras has grown greatly; see [1], [5] e [6]. In this paper we establish a necessary and sufficient condition for n elements of the free n-generator MV-algebra to generate a projective…
We study maximal subalgebras of an arbitrary finite dimensional algebra over a field, and obtain full classification/description results of such algebras. This is done by first obtaining a complete classification in the semisimple case, and…
We study the class of pseudo BL-algebras whose every maximal filter is normal. We present an equational base for this class and we extend these results for the class of basic pseudo hoops with fixed strong unit.
We prove that for all $n$, simultaneously, we can choose prime filtrations of $R/I^n$ such that the set of primes appearing in these filtrations is finite.
We are interested in generalizing part of the theory of ultrafilters on omega to larger cardinals. Here we set the scene for further investigations introducing properties of ultrafilters in strong sense dual to being normal.
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
An MV-module is an MV-algebra endowed with a scalar multiplication with scalars in a PMV-algebra (i.e. an MV-algebra endowed with a binary "ring-like" product). We investigate the class of semisimple MV-modules over a semisimple and totally…
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 prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…
This is a survey of what is known and/or conjectured about the prime and primitive spectra of quantum algebras, of quantized coordinate rings in particular. The topological structure of these spectra, their relations to classical affine…
We describe an $E_k$-cell structure on the free $E_{k+1}$-algebra on a point, and more generally describe how the May-Milgram filtration of $\Omega^m \Sigma^m S^{k}$ lifts to a filtration of the free $E_{k+m}$-algebra on a point by iterated…
In this paper we review some of the main achievements of the semiring-theoretic approach to MV-algebras initiated and pursued mainly by the present authors and their collaborators. The survey focuses mainly on the connections between…
In this paper, we introduce the concept of filter on IL-algebra. It is proved that this concept generalizes the notion of filter on Residuated Lattices. Prime filters on IL-algebra are defined and few interesting properties are obtained. It…
We determine the profinite completions of MV-algebras, and obtain a description that generalizes the well known profinite completions of Boolean algebras as the power sets of their Stone spaces. We also use the description found to…
We characterize all profinite MV-algebras, these are MV-algebras that are inverse limits of finite MV-algebras. It is shown that these are exactly direct product of finite \L ukasiewicz's chains. We also prove that the category $\mathbb{M}$…
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial…
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…
We begin to study the structure of Leibniz algebras having maximal cyclic subalgebras