PBZ*-Lattices: Structure Theory and Subvarieties
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Publication date: 20.08.2020
Reports on Mathematical Logic, 2020, Number 55, pp. 3 - 39
https://doi.org/10.4467/20842589RM.20.001.12433Authors
PBZ*-Lattices: Structure Theory and Subvarieties
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: Reports on Mathematical Logic, 2020, Number 55, pp. 3 - 39
Article type: Original article
Titles:
PBZ*-Lattices: Structure Theory and Subvarieties
PBZ*-Lattices: Structure Theory and Subvarieties
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
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English