Isotopic algebras with nonisomorphic congruence lattices.
type: Item
instance of: scholarly article
title: Isotopic algebras with nonisomorphic congruence lattices.
zbMATH Open document ID: 1307.08001
published in: Algebra Universalis
publication date: 2014-11-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1301.7481
review text: For algebras \(\mathbf A,\mathbf B,\mathbf C\) of the same type, \(\mathbf A\) is said to be isotopic to \(\mathbf B\) over \(\mathbf C\) (\(\mathbf A\sim_{\mathbf C}\mathbf B\)) if there is an isomorphism \(\varphi\colon\mathbf A\times\mathbf C\to\mathbf B\times\mathbf C\) such that, whenever \(a\in\mathbf A\), \(c\in\mathbf C\), there exists \(b\in\mathbf B\) with \(\varphi(a,c)=(b,c)\). The algebras \(\mathbf A\) and \(\mathbf B\) are called isotopic (\(\mathbf A\sim\mathbf B\)), if \(\mathbf A\sim_{\mathbf C}\mathbf B\) for some algebra \(\mathbf C\). The implication \(\mathbf A\sim\mathbf B\Rightarrow\mathrm{Con\,}\mathbf A\cong\mathrm{Con\,}\mathbf B\) is valid in any congruence modular variety. The author describes a class of algebras, in which this implication fails to hold.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 06B10
Mathematics Subject Classification ID: 08A60
zbMATH DE Number: 6369495
zbMATH Keywords: finite algebras
zbMATH Keywords: isotopies
zbMATH Keywords: isotopic algebras
zbMATH Keywords: congruence lattices
reviewed by: Danica Jakubiková-Studenovská
MaRDI profile type: Publication
OpenAlex ID: W2031624097
arXiv ID: 1301.7481
cites work: Q3751631
DOI: 10.1007/S00012-014-0301-4
author: William Demeo
description: scientific article; zbMATH DE number 6369495