Lattice tensor products. II: Ideal lattices
type: Item
instance of: scholarly article
title: Lattice tensor products. II: Ideal lattices
zbMATH Open document ID: 1012.06006
DOI: 10.1023/A:1020850910989
author: Yanyan Li
published in: Acta Mathematica Hungarica
publication date: 2003-05-18T00:00:00Z
review text: [For Part I see ibid. 95, 261-279 (2002; Zbl 0997.06002).] The concept of a lattice tensor product \(A\boxtimes B\) was recently introduced by \textit{G. Grätzer} and \textit{F. Wehrung} [J. Algebra 221, 315-344 (1999; Zbl 0961.06005)]. It is shown in this paper that if \(A\) is a finite lattice then \(A\boxtimes B\) is a subset of the direct power \(B^A\), and it provides an effective criterion for \(A\)-tuples of elements of \(B\) to occur in this representation. This enables the authors to prove the following result on ideal lattices: Theorem. Let \(A\), \(B\) be lattices. If \(A\) is finite then \(\text{Id}(A\boxtimes B)\cong A\boxtimes \text{Id}B\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B05
Mathematics Subject Classification ID: 06B10
zbMATH DE Number: 1912078
zbMATH Keywords: lattice
zbMATH Keywords: tensor product
zbMATH Keywords: lattice tensor product
zbMATH Keywords: Boolean triple construction
zbMATH Keywords: congruence-preserving extension
MaRDI profile type: Publication
full work available at URL: a:1020850910989
OpenAlex ID: W1979137583
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description: scientific article; zbMATH DE number 1912078