PBZ*-Lattices: Structure Theory and Subvarieties

Roberto Giuntini,

Claudia Mureşan,

Francesco Paoli


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.

Słowa kluczowe: orthomodular lattice, PBZ*-lattice, Brouwer-Zadeh lattice, Kleene lattice, unsharp quantum theory, subtractive variety

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