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Izvestiya: Mathematics, 2014, Volume 78, Issue 5, Pages 922–936
DOI: https://doi.org/10.1070/IM2014v078n05ABEH002713 (Mi im8146) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Alternative algebras admitting derivations with invertible values and invertible derivations

I. B. Kaygorodovab, Yu. S. Popovac

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Universidade de São Paulo, Instituto de Matemática e Estatística
c Novosibirsk State University
English version PDF (278 kB) Citations (18)
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DOI: https://doi.org/10.1070/IM2014v078n05ABEH002713
Abstract: We prove an analogue of the Bergen–Herstein–Lanski theorem for alternative algebras: describe all alternative algebras that admit derivations with invertible values. We also prove an analogue of Moens' theorem for alternative algebras (a finite-dimensional alternative algebra over a field of characteristic zero is nilpotent if and only if it admits an invertible Leibniz derivation).
Keywords: derivation, alternative algebra, nilpotent algebra.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-31122
14-01-31084
Ministry of Education and Science of the Russian Federation МК-330.2013.1
Fundação de Amparo à Pesquisa do Estado de São Paulo 2011/51132-9
Received: 15.07.2013
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2014, Volume 78, Issue 5, Pages 75–90
DOI: https://doi.org/10.4213/im8146
Bibliographic databases:
Document Type: Article
UDC: 512.554.5
MSC: 17A36, 17D05
Language: English
Original paper language: Russian
Citation: I. B. Kaygorodov, Yu. S. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izv. Math., 78:5 (2014), 922–936
Citation in format AMSBIB
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\by I.~B.~Kaygorodov, Yu.~S.~Popov
\paper Alternative algebras admitting derivations with invertible values and invertible derivations
\jour Izv. Math.
\yr 2014
\vol 78
\issue 5
\pages 922--936
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  • https://doi.org/10.1070/IM2014v078n05ABEH002713
  • https://www.mathnet.ru/eng/im/v78/i5/p75
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:597
    Russian version PDF:265
    English version PDF:16
    References:88
    First page:45
     
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