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PBZ*-Lattices: Structure Theory and Subvarieties

Publication date: 20.08.2020

Reports on Mathematical Logic, 2020, Number 55, pp. 3 - 39

https://doi.org/10.4467/20842589RM.20.001.12433

Authors

,
Roberto Giuntini
Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy
All publications →
,
Claudia Mureşan
Faculty of Mathematics and Computer Science, University of Bucharest, Romania
All publications →
Francesco Paoli
Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy
All publications →

Titles

PBZ*-Lattices: Structure Theory and Subvarieties

Abstract

We investigate the structure theory of the variety of PBZ*-lattices and some of its proper subvarieties. These lattices with additional structure originate in the foundations of quantum mechanics and can be viewed as a common generalisation of orthomodular lattices and Kleene algebras expanded by an extra unary operation. We lay down the basics of the theories of ideals and of central elements in PBZ*-lattices, we prove some structure theorems, and we explore some connections with the theories of subtractive and binary discriminator varieties.

AMS Subject Classification: primary 08B15; secondary 06B10, 08B26, 03G25, 03G12.

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Information

Information: Reports on Mathematical Logic, 2020, Number 55, pp. 3 - 39

Article type: Original article

Titles:

Polish:

PBZ*-Lattices: Structure Theory and Subvarieties

English:

PBZ*-Lattices: Structure Theory and Subvarieties

Authors

Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy

Faculty of Mathematics and Computer Science, University of Bucharest, Romania

Department of Pedagogy, Psychology and Philosophy, University of Cagliari, Italy

Published at: 20.08.2020

Received at: 31.01.2019

Article status: Open

Licence: CC BY-NC-ND  licence icon

Percentage share of authors:

Roberto Giuntini (Author) - 33%
Claudia Mureşan (Author) - 33%
Francesco Paoli (Author) - 34%

Article corrections:

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Publication languages:

English

View count: 1339

Number of downloads: 974

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