State BCK-algebras and state-morphism BCK-algebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F14%3A33151118" target="_blank" >RIV/61989592:15310/14:33151118 - isvavai.cz</a>
Result on the web
<a href="http://www.sciencedirect.com/science/article/pii/S0165011413004934" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0165011413004934</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2013.12.007" target="_blank" >10.1016/j.fss.2013.12.007</a>

Result language
angličtina
Original language name
State BCK-algebras and state-morphism BCK-algebras
Original language description
In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-algebra extending the language of BCK-algebras by adding a unary operator which models probabilistic reasoning. We present a relation between state operators and state-morphism operators and measures and states on BCK-algebras, respectively. We study subdirectly irreducible state (morphism) BCK-algebras. We introduce the concept of an adjoint pair in BCK-algebras and show that there is a one-to-one correspondence betweenadjoint pairs and state-morphism operators. In addition, we show the generators of quasivarieties of state-morphism BCK-algebras.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/EE2.3.20.0051" target="_blank" >EE2.3.20.0051: Algebraic methods in Quantum Logic</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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