MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS

Zdenka Riečanová, Jiří Janda

Abstract


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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This work is licensed under a Creative Commons Attribution 4.0 International License.

ISSN 1210-2709 (Print)
ISSN 1805-2363 (Online)
Published by the Czech Technical University in Prague