Riesz Space-Valued States on Pseudo MV-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73589844" target="_blank" >RIV/61989592:15310/18:73589844 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Riesz Space-Valued States on Pseudo MV-algebras
Original language description
We introduce Riesz space-valued states, called (R, 1(R))-states, on a pseudo MV-algebra, where R is a Riesz space with a fixed strong unit 1(R). Pseudo MV-algebras are a non-commutative generalization of MV-algebras. Such a Riesz space-valued state is a generalization of usual states on MV-algebras. Any (R, 1(R))-state is an additive mapping preserving a partial addition in pseudo MV-algebras. We introduce (R, 1(R))-state-morphisms and extremal (R, 1(R))-states, and we study relations between them. We study metrical completion of unital l-groups with respect to an (R, 1(R))-state. If the unital Riesz space is Dedekind complete, we study when the space of (R, 1(R))-states is a Choquet simplex or even a Bauer simplex.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-15286S" target="_blank" >GA15-15286S: Algebraic, many-valued and quantum structures for uncertainty modelling</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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