Coverings in the lattice of \(\ell\)-varieties
type: Item
instance of: scholarly article
title: Coverings in the lattice of \(\ell\)-varieties
zbMATH Open document ID: 0536.06015
DOI: 10.1007/BF01979648
author: N. Ya. Medvedev
published in: Algebra and Logic
publication date: 1983-01-01T00:00:00Z
review text: A variety \(V\) of \(\ell\)-groups (\(\ell\)-variety) is said to be 0-approximable if \((x\wedge y^{-1}x^{-1}y)\vee e=e\) holds for every \(x,y\in G\) and \(G\in V\). The class \(L_0\) of all 0-approximable \(\ell\)-varieties is a lattice with respect to the naturally defined operations of sup and inf. Let \(\bar V, V\in L_0\). Then \(\bar V\) is said to cover \(V\) in \(L_0\) if \(\bar V\supseteq V\) and if \(\bar V\supseteq U\supseteq V\) for some \(U\in L_0\) implies \(U=\bar V\) or \(U=V\). In the present paper the existence of \(2^{\omega_0}\) 0-approximable \(\ell\)-varieties is proved which have \(2^{\omega_0}\) different coverings in the lattice \(L_0\).
reviewed by: František Šik
Mathematics Subject Classification ID: 06F15
Mathematics Subject Classification ID: 08B15
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 3851173
zbMATH Keywords: variety of \(\ell\)-groups
zbMATH Keywords: 0-approximable \(\ell\)-varieties
zbMATH Keywords: coverings
MaRDI profile type: Publication
cites work: Relatively convex subgroups of orderable groups
cites work: Q5586432
cites work: Q3936792
cites work: Q4002576
cites work: An uncountable tower of \(\ell\)-group varieties
cites work: Convergence and Cauchy Structures on Lattice Ordered Groups
full work available at URL: https://doi.org/10.1007/bf01979648
OpenAlex ID: W1981130448
description: scientific article; zbMATH DE number 3851173