A non-capped tensor product of lattices.
type: Item
instance of: scholarly article
title: A non-capped tensor product of lattices.
zbMATH Open document ID: 1308.06002
author: Bogdan Chornomaz
published in: Algebra Universalis
publication date: 2015-01-09T00:00:00Z
review text: Tensor product for join-semilattices was introduced by \textit{J. A. Anderson} and \textit{N. Kimura} [Semigroup Forum 16, 83-88 (1978; Zbl 0387.20044)], and by \textit{G. A. Fraser} [Trans. Am. Math. Soc. 217, 183-194 (1976; Zbl 0355.06013)]. If \(A\), \(B\) are lattices then their tensor product need not be a lattice but only a join-semilattice. However, if the tensor product of \(A\) and \(B\) is capped then it is a lattice. Whether the converse is true was an open problem posed by \textit{G. Grätzer} and \textit{F. Wehrung} [J. Pure Appl. Algebra 147, No. 3, 273-301 (2000; Zbl 0945.06003)]. The aim of this paper is to construct a tensor product of lattices \(A\) and \(B\) which is a lattice despite the fact that it is not capped. In this construction, \(A\) has length three and is generated by a nine-element set of atoms, while \(B\) is the dual of \(A\).
reviewed by: Ivan Chajda
Mathematics Subject Classification ID: 06B05
zbMATH DE Number: 6384895
zbMATH Keywords: tensor products of lattices
zbMATH Keywords: semilattices
zbMATH Keywords: capped lattices
MaRDI profile type: Publication
full work available at URL: s00012-014-0304-1
OpenAlex ID: W2003994576
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cites work: Q4834373
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DOI: 10.1007/S00012-014-0304-1
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description: scientific article; zbMATH DE number 6384895