Geodesic
Generalized homogeneous, prelattice and MV-effect algebras
Kybernetika, Tome 41 (2005) no. 2, p. [129]

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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.
Classification : 03B50, 03G12, 03G25, 06D35, 81P10
Keywords: effect algebra; generalized effect algebra; generalized MV- effect algebra; prelattice and homogeneous generalized effect algebra 
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     author = {Rie\v{c}anov\'a, Zdenka and Marinov\'a, Ivica},
     title = {Generalized homogeneous, prelattice and {MV-effect} algebras},
     journal = {Kybernetika},
     pages = {[129]},
     publisher = {mathdoc},
     volume = {41},
     number = {2},
     year = {2005},
     mrnumber = {2138764},
     zbl = {1249.03122},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2005__41_2_a2/}
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Riečanová, Zdenka; Marinová, Ivica. Generalized homogeneous, prelattice and MV-effect algebras. Kybernetika, Tome 41 (2005) no. 2, p. [129]. http://geodesic.mathdoc.fr/item/KYB_2005__41_2_a2/