Aten, Charlotte
Published in
Algebra universalis

We study a class of algebras we regard as generalized rock–paper–scissors games. We determine when such algebras can exist, show that these algebras generate the varieties generated by hypertournament algebras, count these algebras, study their automorphisms, and determine their congruence lattices. We produce a family of finite simple algebras.

Lenzi, Giacomo Di Nola, Antonio
Published in
Algebra universalis

This paper deals with the problem of characterizing those topological spaces which are homeomorphic to the prime spectra of MV-algebras or Abelian ℓ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargi...

Murphy-Hernandez, Frank
Published in
Algebra universalis

For a group G and a poset X, we say that X is a G-poset if it is equipped with a G-action that is monotone. If we consider the mononote G-equivariant maps as morphisms, then we get the category of G-posets. We give a description of the projective objects, injective objects, quotients, and generators.

Hager, Anthony W. Scowcroft, Philip
Published in
Algebra universalis

Within 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}-groups, “H∈W∗\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wa...

Chen, Wei
Published in
Algebra universalis

In this paper, we study semiconic idempotent commutative residuated lattices. An algebra of this kind is a semiconic generalized Sugihara monoid if it is generated by the lower bounds of the monoid identity. We establish a category equivalence between semiconic generalized Sugihara monoids and Brouwerian algebras with a strong nucleus. As an applic...

Galatos, Nikolaos Jipsen, Peter
Published in
Algebra universalis

Generalized bunched implication algebras (GBI-algebras) are defined as residuated lattices with a Heyting implication, and are positioned between Boolean algebras with operators and lattices with operators. We characterize congruences on GBI-algebras by filters that are closed under Gumm–Ursini terms, and for involutive GBI-algebras these terms sim...

Dvurečenskij, Anatolij Lachman, Dominik
Published in
Algebra universalis

We show that under some natural conditions, we are able to lift an n-dimensional spectral resolution from one monotone σ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$...

Bergman, C. Penza, T. Romanowska, A. B.
Published in
Algebra universalis

The Mal’tsev product of two varieties of similar algebras is always a quasivariety. We consider the question of when this quasivariety is a variety. The main result asserts that if V\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage...

Gutiérrez García, Javier Kubiak, Tomasz Picado, Jorge
Published in
Algebra universalis

The purpose of this paper is to identify the role of perfectness in the Michael insertion theorem for perfectly normal locales. We attain it by characterizing perfect locales in terms of strict insertion of two comparable lower semicontinuous and upper semicontinuous localic real functions. That characterization, when combined with the insertion th...

Gao, Meng Zhang, Wen Ting Luo, Yan Feng
Published in
Algebra universalis

Since the 1970s, the smallest known non-finitely based involution semigroups are of order six. This paper exhibits the first example of a non-finitely based involution semigroup of order five.