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Izv. RAN. Ser. Mat., 2014, Volume 78, Issue 5, Pages 75–90 (Mi izv8146)  

This article is cited in 12 scientific papers (total in 12 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

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

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/im8146

Full text: PDF file (541 kB)
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English version:
Izvestiya: Mathematics, 2014, 78:5, 922–936

Bibliographic databases:

UDC: 512.554.5
MSC: 17A36, 17D05
Received: 15.07.2013

Citation: I. B. Kaygorodov, Yu. S. Popov, “Alternative algebras admitting derivations with invertible values and invertible derivations”, Izv. RAN. Ser. Mat., 78:5 (2014), 75–90; Izv. Math., 78:5 (2014), 922–936

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Macedo Ferreira B.L., Guzzo Jr H., Ferreira R.N., Wei F., “Jordan Derivations of Alternative Rings”, Commun. Algebr.  crossref  isi
    2. Ferreira Bruno Leonardo Macedo, Kaygorodov I., “Commuting Maps on Alternative Rings”, Ric. Mat.  crossref  isi
    3. Macedo Ferreira B.L., Guzzo Jr. Henrique, Wei F., “Multiplicative Lie-Type Derivations on Alternative Rings”, Commun. Algebr.  crossref  mathscinet  isi
    4. I. Kaygorodov, E. Okhapkina, “$\delta$-Derivations of semisimple finite-dimensional structurable algebras”, J. Algebra and Appl., 13:4 (2014), 1350130, 12 pp.  crossref  mathscinet  zmath  isi  scopus
    5. I. Kaygorodov, Yu. Popov, “Generalized derivations of (color) $n$-ary algebras”, Linear and Multilinear Algebra, 64:6 (2016), 1086–1106  crossref  mathscinet  zmath  isi  scopus
    6. I. Kaygorodov, Yu. Popov, “A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations”, J. Algebra, 456 (2016), 323–347  crossref  mathscinet  zmath  isi  scopus
    7. V. N. Zhelyabin, A. I. Shestakov, “Alternative and Jordan algebras admitting ternary derivations with invertible values”, Sib. elektron. matem. izv., 14 (2017), 1505–1523  mathnet  crossref
    8. I. Kaygorodov, “On the Kantor product”, J. Algebra Appl., 16:9 (2017), 1750167, 17 pp.  crossref  mathscinet  zmath  isi  scopus
    9. I. Kaygorodov, A. Lopatin, Yu. Popov, “Jordan algebras admitting derivations with invertible values”, Comm. Algebra, 46:1 (2018), 69–81  crossref  mathscinet  zmath  isi  scopus
    10. I. Kaygorodov, A. Lopatin, Yu. Popov, “The structure of simple noncommutative Jordan superalgebras”, Mediterr. J. Math., 15:2 (2018), UNSP 33, 20 pp.  crossref  mathscinet  isi  scopus
    11. Devi G.L., Jayalakshmi K., “Derivations With Invertible Values in Flexible Algebras”, Bol. Soc. Parana. Mat., 38:6 (2020), 63–71  crossref  isi
    12. Artemovych O.D., Bovdi V.A., Salim M.A., “Derivations of Group Rings”, Acta Sci. Math., 86:1-2 (2020), 51–72  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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