MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS
We show that in any generalized effect algebra (G;⊕, 0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;⊕, 0), called a summability block. If G is lattice ordered, then every summability block in G is a generalized MV-effect algebra. Moreover, if every element of G h...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
CTU Central Library
2013-10-01
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| Series: | Acta Polytechnica |
| Online Access: | https://ojs.cvut.cz/ojs/index.php/ap/article/view/1865 |
| Summary: | We show that in any generalized effect algebra (G;⊕, 0) a maximal pairwise summable subset is a sub-generalized effect algebra of (G;⊕, 0), called a summability block. If G is lattice ordered, then every summability block in G is a generalized MV-effect algebra. Moreover, if every element of G has an infinite isotropic index, then G is covered by its summability blocks, which are generalized MV-effect algebras in the case that G is lattice ordered. We also present the relations between summability blocks and compatibility blocks of G. Counterexamples, to obtain the required contradictions in some cases, are given. |
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| ISSN: | 1210-2709 1805-2363 |