Modular elements in congruence lattices of \(G\)-sets
type: Item
instance of: scholarly article
title: Modular elements in congruence lattices of \(G\)-sets
zbMATH Open document ID: 0953.08001
published in: Beiträge zur Algebra und Geometrie
publication date: 2000-05-02T00:00:00Z
full work available at URL: https://eudml.org/doc/231325
full work available at URL: BAG
review text: Let \(A\) be a nonvoid set and \(\varphi\) a homomorphism from a group \(G\) into the full transformation group of \(A\). Then \(A\) with the set of unary operations \(g(a)= (\varphi(g))(a)\), \(a\in A\), \(g\in G\), on \(A\) is called a \(G\)-set. An element \(x\) in a lattice \(L\) is called modular if \((x\vee y)\wedge z= (x\wedge z)\vee y\) for \(y,z\in L\), \(y\leq z\). The aim of the paper is to describe modular elements in congruence lattices of \(G\)-sets.
Mathematics Subject Classification ID: 08A30
Mathematics Subject Classification ID: 08A60
Mathematics Subject Classification ID: 06C05
zbMATH DE Number: 1428663
zbMATH Keywords: \(G\)-set
zbMATH Keywords: modular elements
zbMATH Keywords: congruence lattices
author: Boris Vernikov
reviewed by: Jaromír Duda
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1428663