TY - JOUR
AU - Riečanová, Zdenka
AU - Janda, Jiří
PY - 2013/10/24
Y2 - 2023/09/29
TI - MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS
JF - Acta Polytechnica
JA - Acta Polytech
VL - 53
IS - 5
SE - Articles
DO - 10.14311/AP.2013.53.0457
UR - https://ojs.cvut.cz/ojs/index.php/ap/article/view/1865
SP - 457-461
AB - 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.
ER -