Wehrung, Friedrich

It is well known that the real spectrum of any commutative unital ring, and the ℓ-spectrum of any Abelian lattice-ordered group with order-unit, are all completely normal spectral spaces. We prove the following results: (1) Every real spectrum can be embedded, as a spectral subspace, into some ℓ-spectrum. (2) Not every real spectrum is an ℓ-spectru...

Wehrung, Friedrich

A compact topological space X is spectral if it is sober (i.e., every irreducible closed set is the closure of a unique singleton) and the compact open subsets of X form a basis of the topology of X, closed under finite intersections. Theorem. A topological space X is homeomorphic to the spectrum of some countable Abelian ℓ-group with unit (resp., ...

Wehrung, Friedrich

The problem of determining the range of a given functor arises in various parts of mathematics.We present a sample of such problems, with focus on various functors, arising in the contexts of nonstable K_0-theory of rings, congruence lattices of universal algebras, spectral spaces of ring-like objects.We also sketch some of the ideas involved in th...

Marra, Vincenzo
Published in
Mathematica Slovaca

An MV-algebra (equivalently, a lattice-ordered Abelian group with a distinguished order unit) is strongly semisimple if all of its quotients modulo finitely generated congruences are semisimple. All MV-algebras satisfy a Chinese Remainder Theorem, as was first shown by Keimel four decades ago in the context of lattice-groups. In this note we prove ...

Hofmann, Dirk Nora, Pedro
Published in
Algebra universalis

In this paper, we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by the Cartesian product on the relati...

Schwartz, Niels
Published in
Algebra universalis

A frame is a complete distributive lattice that satisfies the infinite distributive law b∧⋁i∈Iai=⋁i∈Ib∧ai\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${b \wedge \bigv...

Darnel, Michael R. Martinez, Jorge
Published in
Order

For a given class T of compact Hausdorff spaces, let Y(T) denote the class of ℓ-groups G such that for each g∈G, the Yosida space Y(g) of g belongs to T. Conversely, if R is a class of ℓ;-groups, then T(R) stands for the class of all spaces which are homeomorphic to a Y(g) for some g∈G∈R. The correspondences T↦Y(T) and R↦T(R) are examined with rega...