Pulmannová, Sylvia Divisible effect algebras and interval effect algebras. (English) Zbl 1052.03040 Commentat. Math. Univ. Carol. 42, No. 2, 219-236 (2001). 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. Reviewer: Josef Tkadlec (Praha) Cited in 3 Documents MSC: 03G12 Quantum logic 81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects) 06F15 Ordered groups Keywords:divisible effect algebra; interval effect algebra; partially ordered group PDFBibTeX XMLCite \textit{S. Pulmannová}, Commentat. Math. Univ. Carol. 42, No. 2, 219--236 (2001; Zbl 1052.03040) Full Text: EuDML