ORTHOGONAL SETS IN EFFECT ALGEBRAS

Abstract

We show that for a lattice effect algebra two conceptions of completeness (cr-completeness) coincide. Moreover, a separable effect algebra is complete if and only if it is cr-complete. Further, in an Archimedean atomic lattice effect algebra to every nonzero element x there is a -orthogonal system G of not necessary different atoms such that x = G. A lattice effect algebra E is complete if and only if every block of E is complete. Every atomic Archimedean lattice effect algebra is a union of atomic blocks, since each of its elements is a sum of a -orthogonal system of atoms.