Generalized homogeneous, prelattice and MV-effect algebras

Riečanová, Zdena, and Marinová, Ivica. "Generalized homogeneous, prelattice and MV-effect algebras." Kybernetika 41.2 (2005): [129]-142. <http://eudml.org/doc/33745>.

@article{Riečanová2005,
abstract = {We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra $P$ are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra $P$ is a union of generalized MV-effect algebras and every generalized homogeneous effect algebra is a union of its maximal sub-generalized effect algebras with hereditary Riesz decomposition property (blocks). Properties of sharp elements, the center and center of compatibility of $P$ are shown. We prove that on every generalized MV-effect algebra there is a bounded orthogonally additive measure.},
author = {Riečanová, Zdena, Marinová, Ivica},
journal = {Kybernetika},
keywords = {effect algebra; generalized effect algebra; generalized MV- effect algebra; prelattice and homogeneous generalized effect algebra; effect algebra; generalized effect algebra; generalized MV-effect algebra; prelattice},
language = {eng},
number = {2},
pages = {[129]-142},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalized homogeneous, prelattice and MV-effect algebras},
url = {http://eudml.org/doc/33745},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Riečanová, Zdena
AU - Marinová, Ivica
TI - Generalized homogeneous, prelattice and MV-effect algebras
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 2
SP - [129]
EP - 142
AB - We study unbounded versions of effect algebras. We show a necessary and sufficient condition, when lattice operations of a such generalized effect algebra $P$ are inherited under its embeding as a proper ideal with a special property and closed under the effect sum into an effect algebra. Further we introduce conditions for a generalized homogeneous, prelattice or MV-effect effect algebras. We prove that every prelattice generalized effect algebra $P$ is a union of generalized MV-effect algebras and every generalized homogeneous effect algebra is a union of its maximal sub-generalized effect algebras with hereditary Riesz decomposition property (blocks). Properties of sharp elements, the center and center of compatibility of $P$ are shown. We prove that on every generalized MV-effect algebra there is a bounded orthogonally additive measure.
LA - eng
KW - effect algebra; generalized effect algebra; generalized MV- effect algebra; prelattice and homogeneous generalized effect algebra; effect algebra; generalized effect algebra; generalized MV-effect algebra; prelattice
UR - http://eudml.org/doc/33745
ER -