Orthogonal sets in effect algebras (Q2757022)
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scientific article; zbMATH DE number 1675679
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Orthogonal sets in effect algebras |
scientific article; zbMATH DE number 1675679 |
Statements
14 July 2002
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effect algebra
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orthogonal system
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completeness
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MV-algebra
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0.9199668
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0.88133544
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0.87716305
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0.86969566
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0.86537075
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0.86398864
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0.86375713
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Orthogonal sets in effect algebras (English)
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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.
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