Splitting in the variety of residuated lattices
type: Item
instance of: scholarly article
title: Splitting in the variety of residuated lattices
zbMATH Open document ID: 1015.08008
author: Tomasz Kowalski
author: Hiroakira Ono
published in: Algebra Universalis
publication date: 2003-04-23T00:00:00Z
review text: A pair \(( {\mathcal V}_1, {\mathcal V}_2)\) of subvarieties of a variety \(\mathcal V\) is called a splitting pair if \({\mathcal V}_1 \not \subseteq {\mathcal V}_2\) and for any subvariety \(\mathcal S\) of \(\mathcal V\) either \({\mathcal V}_1 \subseteq \mathcal S\) or \({\mathcal S} \subseteq {\mathcal V}_2\). In such a case, \({\mathcal V}_1\) is generated by an \(SI\)-algebra which is called a splitting algebra. The authors show that the only algebra that splits the lattice of subvarieties of the variety of residuated lattices is the two-element Boolean algebra.
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 1899967
zbMATH Keywords: residuated lattice
zbMATH Keywords: equationally definable principal congruences
zbMATH Keywords: splitting algebra
MaRDI profile type: Publication
full work available at URL: s000120050187
OpenAlex ID: W1999787898
DOI: 10.1007/S000120050187
description: scientific article; zbMATH DE number 1899967