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 or- thomodular 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.