An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F06%3A00003268" target="_blank" >RIV/61989592:15310/06:00003268 - isvavai.cz</a>
Alternative codes found
RIV/61989592:15310/06:00002565
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
An answer to Demirci's open question, a clarification of his result, and a correction of his interpretation of the result
Original language description
In his note (this issue of this journal), Demirci shows that fields with fuzzy equalities have only trivial fuzzy equalities, concludes that "Therefore, in case L-algebras contain field structure, all results in [1-4] are evident from their classical counterparts.", and asks a question "does there exist any L-algebra with an L-equality different from trivial L-equalities in case the ordinary part of the L-algebra includes two binary operations that define group, ring, module or vector space structure?".In our reply, we show the following. First, by presenting examples of group-based L-algebras with nontrivial L-equalities, we show that the answer to Demirci's question is positive. Second, we clarify the meaning of Demirci's result and show that it isin fact a natural generalization of the well-known classical result saying that ordinary fields do not have non-trivial congruences. Third, we argue that Demirci's interpretation of his result is mistaken and that it is
Czech name
Odpověď na Demirciho otevřené otázky, objasnění jeho výsledků a oprava jeho interpretace dosažených výsledků
Czech description
Výsledky zkoumání Demirciho otevřené otázky, objasnění jeho výsledků a oprava jeho interpretace dosažených výsledků

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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Project
<a href="/en/project/KJB1137301" target="_blank" >KJB1137301: Relational systems in presence of vagueness and uncertainty:mathematical foundations for applications</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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