An approach to orthomodular lattices via lattices with an antitone involution-Reference-Cited by-同舟云学术

An approach to orthomodular lattices via lattices with an antitone involution

Published:2016-08-01 Issue:4 Volume:66 Page:773-780
ISSN:1337-2211
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Chajda Ivan¹,Radeleczki Sándor²

Affiliation:

1. Department of Algebra and Geometry Faculty of Science Palacký University 17. Listopadu 12 77146 Olomouc Czech Republic

2. Institute of Mathematics University of Miskolc H-3515 Miskolc-Egyetemváros Hungary

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2015-0179/pdf

Reference16 articles.

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3. Birkhoff, G.: Lattice Theory (3rd ed.). Amer. Math. Soc. Colloq. Publ. 25, Amer. Math. Soc., Providence, RI, 1967.

4. Birkhoff, G.—Von Neumann, J.: The logics of quantum mechanics, Ann. of Math. (2) 37 (1936), 823–834.

5. Chajda, I.: Lattices and semilattices having an antitone involution in every upper interval, Comment. Math. Univ. Carolin. 44 (2003), 577–585.

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