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

J 2011

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

PASEKA, Jan a Zdenka RIEČANOVÁ

Základní údaje

Originální název

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

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí) a Zdenka RIEČANOVÁ (703 Slovensko)

Vydání

Soft computing, Springer-Verlag GmbH, 2011, 1432-7643

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.880

Kód RIV

RIV/00216224:14310/11:00055100

Organizační jednotka

Přírodovědecká fakulta

DOI

https://doi.org/10.1007/s00500-010-0561-7

UT WoS

000287451000012

Klíčová slova anglicky

Non-classical logics; MV-algebras; Sharply dominating lattice effect algebras; Basic decomposition of elements; Bifull sub-lattice effect algebras; States

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 10. 4. 2012 18:27, prof. RNDr. Jan Paseka, CSc.

Anotace

V originále

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). Moreover, for compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved. Further, we prove "State smearing theorem" for these lattice effect algebras.

Návaznosti

MSM0021622409, záměr

Název: Matematické struktury a jejich fyzikální aplikace

Investor: Ministerstvo školství, mládeže a tělovýchovy ČR, Matematické struktury a jejich fyzikální aplikace

Citovat

PASEKA, Jan a Zdenka RIEČANOVÁ. The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states. Soft computing. Springer-Verlag GmbH, 2011, roč. 15, č. 3, s. 543-555. ISSN 1432-7643. Dostupné z: https://doi.org/10.1007/s00500-010-0561-7.

@article{967839,
   author = {Paseka, Jan and Riečanová, Zdenka},
   article_number = {3},
   doi = {https://doi.org/10.1007/s00500-010-0561-7},
   keywords = {Non-classical logics; MV-algebras; Sharply dominating lattice effect algebras; Basic decomposition of elements; Bifull sub-lattice effect algebras; States},
   language = {eng},
   issn = {1432-7643},
   journal = {Soft computing},
   title = {The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states},
   url = {http://www.springerlink.com/content/t44107u38q472u54/about/},
   volume = {15},
   year = {2011}
}

TY  - JOUR
ID  - 967839
AU  - Paseka, Jan - Riečanová, Zdenka
PY  - 2011
TI  - The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states
JF  - Soft computing
VL  - 15
IS  - 3
SP  - 543-555
EP  - 543-555
PB  - Springer-Verlag GmbH
SN  - 14327643
KW  - Non-classical logics
KW  - MV-algebras
KW  - Sharply dominating lattice effect algebras
KW  - Basic decomposition of elements
KW  - Bifull sub-lattice effect algebras
KW  - States
UR  - http://www.springerlink.com/content/t44107u38q472u54/about/
L2  - http://www.springerlink.com/content/t44107u38q472u54/about/
N2  - 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). Moreover, for compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved. Further, we prove "State smearing theorem" for these lattice effect algebras.
ER  -

PASEKA, Jan a Zdenka RIEČANOVÁ. The inheritance of BDE-property in sharply dominating lattice effect algebras and (o)-continuous states. \textit{Soft computing}. Springer-Verlag GmbH, 2011, roč.~15, č.~3, s.~543-555. ISSN~1432-7643. Dostupné z: https://doi.org/10.1007/s00500-010-0561-7.

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