Weakly orthomodular and dually weakly orthomodular lattices
type: Item
instance of: scholarly article
title: Weakly orthomodular and dually weakly orthomodular lattices
zbMATH Open document ID: 1441.06005
author: Ivan Chajda
author: Helmut Länger
published in: Order
publication date: 2018-10-09T00:00:00Z
review text: The authors study the varieties of lattices with a unary operation~\('\) satisfying one or two or the following equations: \begin{align*} x= & (x\land y) \lor (x\land (x\land y)')\\ x= & (x\lor y) \land (x\lor (x\lor y)')\,. \end{align*} In ortholattices, any of these equations is equivalent to orthomodularity. However, here the lattice need not be bounded and the complement~\('\) need not be antitone and involutive. Nevertheless, many properties typical for orthomodular lattices can be proved also in this more general case. The corresponding varieties are arithmetical and congruence regular. Generalizations of horizontal sums, commuting elements, and decompositions to direct products are described.
reviewed by: Mirko Navara
Mathematics Subject Classification ID: 06C15
Mathematics Subject Classification ID: 06B20
zbMATH DE Number: 6949481
zbMATH Keywords: weakly orthomodular lattice
zbMATH Keywords: orthomodular lattice
zbMATH Keywords: lattice with complementation
zbMATH Keywords: residuated lattice
zbMATH Keywords: congruence permutability
zbMATH Keywords: congruence regularity
MaRDI profile type: Publication
full work available at URL: s11083-017-9448-x
OpenAlex ID: W2793781500
cites work: Q3222894
cites work: Q4740609
cites work: A note on orthomodular lattices
cites work: Q4508551
cites work: Q4807556
cites work: Residuation in orthomodular lattices
cites work: Orthomodular lattices can be converted into left residuated l-groupoids
cites work: Q4750696
DOI: 10.1007/S11083-017-9448-X
description: scientific article; zbMATH DE number 6949481