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Ring-like structures with unique symmetric difference related to quantum logic. (English) Zbl 1014.81003
The authors study ring-like quantum structures (so-called generalized Boolean quasirings) generalizing Boolean rings. Particular attention is paid to those structures in which the two normal forms of the symmetric difference in Boolean algebras coincide. This property is related to associativity and weak associativity (which means $$(1+x)+y=1+(x+y)$$). Possible physical interpretation is proposed by presenting a model based on generalized Boolean quasirings and following Mackey’s approach to axiomatic quantum mechanics.

MSC:
 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 03G12 Quantum logic 06E99 Boolean algebras (Boolean rings) 06C15 Complemented lattices, orthocomplemented lattices and posets
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