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Divisible effect algebras and interval effect algebras. (English) Zbl 1052.03040

An effect algebra is called divisible if for each of its elements \(a\) and every positive integer \(n\) there is a unique element \(x\) of the effect algebra such that \(a=nx\). It is shown that divisible effect algebras are interval effect algebras (i.e., representable as intervals of the positive cone in partially ordered abelian groups) proving a one-to-one correspondence with unit intervals in partially ordered rational vector spaces.

MSC:

03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
06F15 Ordered groups
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