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Quantum logics of idempotents of unital rings. (English) Zbl 1317.81010

Summary: We introduce some new examples of quantum logics of idempotents in a ring. We continue the study of symmetric logics, i.e., collections of subsets generalizing Boolean algebras and closed under the symmetric difference.

MSC:

81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
03G05 Logical aspects of Boolean algebras
46L60 Applications of selfadjoint operator algebras to physics
17C27 Idempotents, Peirce decompositions
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