  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.
