Congruence lattices of function lattices
type: Item
instance of: scholarly article
title: Congruence lattices of function lattices
zbMATH Open document ID: 0817.06006
DOI: 10.1007/BF02115812
published in: Order
publication date: 1995-07-27T00:00:00Z
review text: Let \(D\) be a bounded, distributive lattice, \(L\) a lattice. The generalized function lattice \(L[D]\) has as elements the continuous isotone maps of \(X\) into \(L\), where \(X\) is the poset of all prime-filters of \(D\) with the usual topology. The authors show for congruence lattices the isomorphism \(\text{Con }L[D]\cong (\text{Con } L)[\text{Con }D]\) iff \(\text{Con }L\) or \(D\) is finite. \(E[A]\) is complete (or algebraic) for every algebraic lattice \(A\) iff \(E\) is finite.
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 720841
zbMATH Keywords: generalized function lattice
zbMATH Keywords: congruence lattices
zbMATH Keywords: algebraic lattice
author: G. Grätzer
author: E. T. Schmidt
reviewed by: Gudrun Kalmbach
MaRDI profile type: Publication
cites work: Exponents of Finite Simple Lattices
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full work available at URL: https://doi.org/10.1007/bf02115812
OpenAlex ID: W1565628251
description: scientific article; zbMATH DE number 720841