Lattice-ordered pregroups are semi-distributive

We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the distributive law which holds in lattice-ordered pregroups.

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Bibliographic Details
Published in:	Algebra universalis Vol. 82; no. 1
Main Authors:	Galatos, Nick, Jipsen, Peter, Kinyon, Michael, Přenosil, Adam
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-02-2021 Springer Nature B.V
Subjects:	Algebra Mathematics Mathematics and Statistics 06B99 06F05 Residuated lattices Pregroups
Online Access:	Get full text
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Description
Summary:	We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the distributive law which holds in lattice-ordered pregroups.
ISSN:	0002-5240 1420-8911
DOI:	10.1007/s00012-020-00703-4