The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F11%3A00055100" target="_blank" >RIV/00216224:14310/11:00055100 - isvavai.cz</a>
Result on the web
<a href="http://www.springerlink.com/content/t44107u38q472u54/about/" target="_blank" >http://www.springerlink.com/content/t44107u38q472u54/about/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00500-010-0561-7" target="_blank" >10.1007/s00500-010-0561-7</a>
Alternative languages
Result language
angličtina
Original language name
The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
Original language description
We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebras E, namely their blocks M, centers C(E), compatibility centers B(E) and sets of all sharp elements S(E) of E. We show that in every such effect algebra E, everyatomic block M and the set S(E) are bifull sub-lattice effect algebras of E. Consequently, if E is moreover sharply dominating then every atomic block M is again sharply dominating and the basic decompositions of elements (BDE of x) in E and in M coincide. Thus in the compatibility center B(E) of E, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks and in E. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely, we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebra E with B(E) not equal C(E).
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Soft computing
ISSN
1432-7643
e-ISSN
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Volume of the periodical
15
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
13
Pages from-to
543-555
UT code for WoS article
000287451000012
EID of the result in the Scopus database
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