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Sharply dominating effect algebras. (English) Zbl 0939.03073
Summary: Sharply dominating effect algebras are introduced. It is shown that if an effect algebra $$P$$ is sharply dominating, then the set of sharp elements $$P_s$$ in $$P$$ forms an orthoalgebra in $$P$$. It is also shown that if $$P$$ is sharply dominating, then there exists a unique Brouwer-complementation $$\sim$$ on $$P$$ such that the set of BZ-sharp elements $$P_s^\sim$$ coincides with $$P_s$$. Conversely, if $$P$$ is a BZ-effect algebra in which $$P_s^\sim$$ = $$P_s$$, then $$P$$ is sharply dominating. The concept of sharpness on a quotient effect algebra is briefly considered.

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