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PBZ*-lattices : structure theory and subvarieties

Giuntini Roberto, Mureşan Claudia, Paoli Francesco

Reports on Mathematical Logic

2020

Vol. 55

3--39

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.