PBZ*-Lattices: Structure Theory and Subvarieties

Roberto Giuntini; Claudia Mureşan; Francesco Paoli

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arXiv · 1804.08136

PBZ*-Lattices: Structure Theory and Subvarieties

Roberto Giuntini·Claudia Mureşan·Francesco Paoli

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Abstract

We investigate the structure theory of the variety of \emph{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.

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Roberto Giuntini, Claudia Mureşan, Francesco Paoli. 2018-04-22. PBZ*-Lattices: Structure Theory and Subvarieties. https://arxiv.org/abs/1804.08136

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