PBZ*-Lattices: Structure Theory and Subvarieties

Roberto Giuntini, Claudia Mureşan, Francesco Paoli
2020 Reports on Mathematical Logic  
A b s t r a c t. 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
more » ... some connections with the theories of subtractive and binary discriminator varieties.
doi:10.4467/20842589rm.20.001.12433 fatcat:lei2p5utx5dnxisbyqmuogrq4i