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

In an earlier paper we established that every second countable, completely normal spectral space is homeomorphic to the ℓ-spectrum of some Abelian ℓ-group. We extend that result to ℓ-spectra of vector lattices over any countable totally ordered division ring k. Extending our original machinery, about finite lattices of polyhedra, from linear to aff...

Azouzi, Youssef Ben Amor, Mohamed Amine
Published in
Algebra universalis

Let B be an Archimedean reduced f-ring. A positive element ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} in B is said to satisfy the propert...

Boulabiar, Karim Brahmi, Wael
Published in
Algebra universalis

Let G be an archimedean ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\ell}$$\end{document}-group. By an f-representation of G we mean an orthomorphism-valued group...

Ben Amor, Mohamed Amine Boulabiar, Karim
Published in
Algebra universalis

In the beginning of the eighties, Buskes and Holland proved that any archimedean almost f-ring is commutative. One decade later, Steinberg showed that if G and H are ℓ with H archimedean, then any positive bilinear map G × G\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage...

Ball, R. N. Hager, A. W. Johnson, D. G. Kizanis, A.
Published in
Algebra universalis

An archimedean ℓ-group is called epicomplete (or universally σ-complete, or sequentially inextensible) if it is divisible, σ-complete and laterally σ-complete. Various characterizations of such G are known in case the G have weak order units. The “theorem” of the title is a characterization of such G which have no weak order unit; it involves the r...

Madden, James J.
Published in
Algebra universalis

This paper introduces several families of equational classes of unital f-rings that are defined by equations that impose conditions on the elements between 0 and 1. We investigate the portion of the lattice of equational classes of f-rings that involves these classes.

Boulabiar, Karim Hager, Anthony
Published in
Algebra universalis

Let A and B be reduced archimedean f-rings, A with identity e; let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$A\,\mathop \to \limits^\gamma\,B$$\end{document} be a...

Johnson, D. G.
Published in
Algebra universalis

In 1962, the author proved that each reduced archimedean f-ring can be represented as an f-ring of continuous extended real-valued function on a locally compact space. The existence of this representation has proved to be quite useful; however, the proof so obscured the definition of the representing functions that deeper applications have remained...

Martínez, Jorge
Published in
Czechoslovak Mathematical Journal

In an algebraic frame L the dimension, dim(L), is defined, as in classical ideal theory, to be the maximum of the lengths n of chains of primes p0