States on wEMV-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F20%3A73603666" target="_blank" >RIV/61989592:15310/20:73603666 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs40574-020-00233-w" target="_blank" >https://link.springer.com/article/10.1007%2Fs40574-020-00233-w</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s40574-020-00233-w" target="_blank" >10.1007/s40574-020-00233-w</a>

Result language
angličtina
Original language name
States on wEMV-algebras
Original language description
Recently in Dvurecenskij and Zahiri (A variety containing EMV-algebras and Pierce sheaves,), new algebras called wEMV-algebras, which generalize MV-algebras, generalized Boolean algebras and EMV-algebras, were founded, and for these algebras a top element is not assumed a priori. For this class we define a state as a mapping from a wEMV-algebra into the real interval [0, 1] which preserves a kind of subtraction of two comparable elements and attaining the value 1 in some element. It can happen that some wEMV-algebras are stateless, e.g. cancellative ones. We characterize extremal states just as state-morphisms which are wEMV-homomorphisms from an algebra into the real interval [0, 1]. We show that there is a one-to-one correspondence between the set of state-morphisms and the set of maximal ideals having a special property. Moreover, we prove that under some conditions every state on a wEMV-algebra is a weak limit of a net of convex combinations of state-morphisms.
Czech name
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Czech description
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Type
J<sub>SC</sub> - Article in a specialist periodical, which is included in the SCOPUS database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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