Infinite intervals in free lattices
type: Item
instance of: scholarly article
title: Infinite intervals in free lattices
zbMATH Open document ID: 0708.06006
DOI: 10.1007/BF00346132
author: S. Tschantz
published in: Order
publication date: 1990-01-01T00:00:00Z
review text: The subject of free lattices has long been of interest in lattice theory, and the determination of their structure involves some deep and subtle proof techniques. Considerable progress was made in the landmark paper by \textit{R. Freese} and \textit{J. B. Nation} [Trans. Am. Math. Soc. 288, 1-42 (1985; Zbl 0567.06008)], and the current paper was inspired by a question posed by these authors: ``Does every infinite interval in the free lattice FL(X) generated by X have FL(3) as a sublattice?'' This question is answered in the affirmative by proving that for any set Y with {\#}Y\(\leq \#X+\aleph_ 0\), every infinite interval of FL(X) has a sublattice isomorphic to FL(Y). The paper is written in a clear concise manner, explains the underlying issues very nicely, and closes with a discussion of some related open questions.
Mathematics Subject Classification ID: 06B25
zbMATH DE Number: 4162948
zbMATH Keywords: free lattices
zbMATH Keywords: infinite interval
reviewed by: Melvin F. Janowitz
MaRDI profile type: Publication
cites work: Splitting lattices generate all lattices
cites work: Sublattices of a Free Lattice
cites work: Free lattices
full work available at URL: https://doi.org/10.1007/bf00346132
OpenAlex ID: W2060697684
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description: scientific article; zbMATH DE number 4162948