Modular atomic effect algebras and the existence of subadditive states

Zdena Riečanová

Kybernetika (2004)

  • Volume: 40, Issue: 4, page [459]-468
  • ISSN: 0023-5954

Abstract

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Lattice effect algebras generalize orthomodular lattices and M V -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.

How to cite

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Riečanová, Zdena. "Modular atomic effect algebras and the existence of subadditive states." Kybernetika 40.4 (2004): [459]-468. <http://eudml.org/doc/33711>.

@article{Riečanová2004,
abstract = {Lattice effect algebras generalize orthomodular lattices and $MV$-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.},
author = {Riečanová, Zdena},
journal = {Kybernetika},
keywords = {effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion of an effect algebra; effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion},
language = {eng},
number = {4},
pages = {[459]-468},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Modular atomic effect algebras and the existence of subadditive states},
url = {http://eudml.org/doc/33711},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Riečanová, Zdena
TI - Modular atomic effect algebras and the existence of subadditive states
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 4
SP - [459]
EP - 468
AB - Lattice effect algebras generalize orthomodular lattices and $MV$-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
LA - eng
KW - effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion of an effect algebra; effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion
UR - http://eudml.org/doc/33711
ER -

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