MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS

Authors

  • Zdenka Riečanová Department of Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovicova 3, SK-812 19 Bratislava
  • Jiří Janda Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlárská 2, CZ-611 37 Brno

DOI:

https://doi.org/10.14311/AP.2013.53.0457

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.

Downloads

Downloads

Published

2013-10-24

Issue

Section

Articles

How to Cite

Riečanová, Z., & Janda, J. (2013). MAXIMAL SUBSETS OF PAIRWISE SUMMABLE ELEMENTS IN GENERALIZED EFFECT ALGEBRAS. Acta Polytechnica, 53(5), 457-461. https://doi.org/10.14311/AP.2013.53.0457
Received 2013-10-24
Accepted 2013-10-24
Published 2013-10-24