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Lattice properties of ring-like quantum logics. (English) Zbl 0967.03055
Generalized Boolean quasirings are models of quantum logics. They might be defined by means of partial generalized Boolean quasirings which are in a one-to-one correspondence with bounded lattices with an involutory antiautomorphism. Connections between properties of these two structures are studied. Under certain assumptions, the associativity of the $$+$$-operation implies that a Boolean ring is obtained, i.e. the quantum system is classical.

MSC:
 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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