States on weak pseudo EMV-algebras. I. States and states morphisms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F22%3A73616845" target="_blank" >RIV/61989592:15310/22:73616845 - isvavai.cz</a>
Result on the web
<a href="https://obd.upol.cz/id_publ/333196732" target="_blank" >https://obd.upol.cz/id_publ/333196732</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.22111/ijfs.2022.7082" target="_blank" >10.22111/ijfs.2022.7082</a>
Alternative languages
Result language
angličtina
Original language name
States on weak pseudo EMV-algebras. I. States and states morphisms
Original language description
Recently in [17, 18], new algebras, called weak pseudo EMV-algebras, wPEMV-algebras for short, were introduced generalizing pseudo MV-algebras, generalized Boolean algebras and pseudo EMV-algebras. For these algebras a top element is not assumed a priori. For this class of algebras, we define a state as a finitely additive mapping from a wPEMV-algebra into the real interval [0, 1] which preserves a partial addition of two non-interactive elements and attaining the value 1 in some element. It can happen that some commutative wPEMV-algebras are stateless, e.g. cancellative ones. The paper is divided into two parts. Part I deals with basic properties of states and state-morphisms which are wPEMV-homomorphisms from a wPEMV-algebra into the real interval [0, 1] endowed as a commutative wPEMV-algebra. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal and normal ideals having a special property. In Part II, we present an analogue of the Krein-Mil'man theorem applied to the set of states. We characterize the space of the state-morphisms of a wPEMV-algebra without top element as a Hausdorff locally compact space in the weak topology of states and we present its Alexandroff's one-point compactification. Moreover, we give an integral representation of any (finitely additive) state by a unique regular Borel s-additive probability measure.
Czech name
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Czech description
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Classification
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
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Iranian Journal of Fuzzy Systems
ISSN
1735-0654
e-ISSN
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Volume of the periodical
19
Issue of the periodical within the volume
4
Country of publishing house
IR - IRAN, ISLAMIC REPUBLIC OF
Number of pages
15
Pages from-to
1-15
UT code for WoS article
000835534900001
EID of the result in the Scopus database
2-s2.0-85135214549