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An approach to orthomodular lattices via lattices with an antitone involution

  • Ivan Chajda EMAIL logo and Sándor Radeleczki
Published/Copyright: November 3, 2016
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 66 Issue 4

Abstract

Several characterizations of orthomodular lattices based on properties of an antitone involution or on sectional antitone involutions are given. Another approach is based on properties of the implication operation which can be derived in every orthomodular lattice but can be also added to basic operations of a bounded lattice. Finally, we introduce the so-called weakly orthomodular lattice as a generalization of orthomodular lattices.

MSC 2010: Primary 06B05; 06C15; Secondary 03G25
Keywords: bounded lattice; antitone involution; sectional antitone involutions; orthomodular lattice; orthocomplemented lattice; weakly orthomodular lattice; implication

(Communicated by Anatolij Dvurečenskij)

Acknowledgement

The authors would like to thank the referees for their valuable and constructive comments.

References

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Received: 2013-9-17
Accepted: 2014-2-9
Published Online: 2016-11-3
Published in Print: 2016-8-1

© 2016 Mathematical Institute Slovak Academy of Sciences

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https://doi.org/10.1515/ms-2015-0179
Keywords for this article
bounded lattice; antitone involution; sectional antitone involutions; orthomodular lattice; orthocomplemented lattice; weakly orthomodular lattice; implication

Articles in the same Issue

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  5. Research Article
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  9. Research Article
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  11. Research Article
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  13. Research Article
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