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Conditional associativity in orthomodular lattices

Jeannine J. M. Gabriëls
From the journal Mathematica Slovaca


For orthomodular lattices the word problem is still not decided, an important obstacle is the lack of distributivity. But also the absence of the associativity law for operations other than the lattice operations meet and join causes difficulties. In this paper we treat some aspects of associativity in orthomodular lattices.

There are six out of 96 orthomodular operations which are associative. We search for orthomodular lattice operations which fulfil the associative identity under some conditions. Specifically we assume that some arguments commute and identify, for each operation, sufficient conditions under which a triple of elements fulfils the respective associativity identity.

MSC 2010: Primary 06C15

(Communicated by Mirko Navara)


The author thanks the anonymous reviewers for careful proofreading.


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Received: 2015-4-10
Accepted: 2015-9-17
Published Online: 2017-6-5
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences