On Associative Algebras Satisfying the Identity $x^5=0$
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F04%3A03101719" target="_blank" >RIV/68407700:21230/04:03101719 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
On Associative Algebras Satisfying the Identity $x^5=0$
Original language description
We study Kuzmin's conjecture on the index of nilpotency for the variety $M_5$ of associative nil-algebras of degree 5. Due to Vaughan-Lee~cite{vau2} the problem is reduced to that for $k$-generator $M_5$-superalgeb-ras, where $kleq 5$. We confirm Kuzmin's conjecture for 2-generator superalgebras proving that they are nilpotent of degree 15
Czech name
O asociativních algebrách s identitou x^5=0
Czech description
Studujeme předpoklad Kuzmina o indexu nilpotence variety M_5 asociativních nil-algeber stupně 5. Diky Vaughan-Leeovy může být problém redukován na podobný pro k-generované M_5-superalgebry, kde k je menší nebo rovno 5. Potvrzujeme předpoklad Kuzmina pro2-generované superalgebry a dokazujeme, ze jsou nilpotentní s indexem 15.
Classification
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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Result continuities
Project
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Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2004
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Algebra and Discrete Mathematics
ISSN
1726-3255
e-ISSN
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Volume of the periodical
2004
Issue of the periodical within the volume
1
Country of publishing house
UA - UKRAINE
Number of pages
9
Pages from-to
112-120
UT code for WoS article
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EID of the result in the Scopus database
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