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Orthogonal sets in efect algebras

Riecanova Z.

Demonstratio Mathematica

2001

Vol. 34, nr 3

525-532

We show that for a lattice effect algebra two conceptions of completeness (o-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.

Archimedean and block-finite lattice efect algebras

Riecanova Z.

Demonstratio Mathematica

2000

Vol. 33, nr 3

443-452

We show that every complete effect algebra is Archimedean. Moreover, a block-finite lattice effect algebra has the MacNeille completion which is a complete effect algebra iff it is Archimedean. We apply our results to orthomodular lattices.