About: The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states

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About: The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.springerlink.com/content/t44107u38q472u54/about/
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, every atomic 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). 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, every atomic 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). (en)
Title	The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states (en)
skos:prefLabel	The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states (en)
skos:notation	RIV/00216224:14310/11:00055100!RIV12-MSM-14310___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM0021622409)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Paseka, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Masarykova univerzita / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	204831
http://linked.open...ai/riv/idVysledku	RIV/00216224:14310/11:00055100
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Non-classical logics; MV-algebras; Sharply dominating lattice effect algebras; Basic decomposition of elements; Bifull sub-lattice effect algebras; States (en)
http://linked.open.../riv/klicoveSlovo	Basic decomposition of elements Bifull sub-lattice effect algebras MV-algebras Non-classical logics Sharply dominating lattice effect algebras States
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[EF8A06DC9572]
http://linked.open...i/riv/nazevZdroje	Soft computing
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	15
http://linked.open...iv/tvurceVysledku	Paseka, Jan Riečanová, Zdenka
http://linked.open...ain/vavai/riv/wos	000287451000012
http://linked.open...n/vavai/riv/zamer	Matematické struktury a jejich fyzikální aplikace
issn	1432-7643
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1007/s00500-010-0561-7
http://localhost/t...ganizacniJednotka	14310

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