On ring-like structures occurring in axiomatic quantum mechanics. (English) Zbl 0945.03095
Summary: Ring-like partial algebras are studied that correspond to bounded lattices with an involutory antiautomorphism and give rise to certain kinds of quantum logics. Various extensions of the partial algebras to total algebras are investigated. Implications of associativity and distributivity are discussed and relations to the structures of the corresponding lattices are derived.
MSC:
03G12 | Quantum logic |
81P10 | Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) |
08A55 | Partial algebras |