Orthogonal sets in effect algebras. (English) Zbl 0989.03071

Riečanová, Zdenka

Demonstr. Math. 34, No. 3, 525-532 (2001).

A system of (not necessarily different) elements of an effect algebra is called \(\oplus\)-orthogonal if the sum of every finite subsystem exists. The author studies \(\oplus\)-orthogonal systems and shows, e.g., that a separable effect algebra is complete iff it is \(\sigma\)-complete, that a lattice effect algebra is complete iff every of its blocks is complete, and that every element of an Archimedean atomic lattice effect algebra is a sum of a \(\oplus\)-orthogonal system of atoms.

Reviewer: Josef Tkadlec (Praha)

MSC:

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

Keywords:

effect algebra; orthogonal system; completeness; MV-algebra