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Algebra Some Current Trends pp 227–240Cite as

On the nilpotency of nil algebras

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References

  1. A.G. Kurosh. Problems in ring theory which are related to the Burnside problem on periodic groups (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 5 (1941), 233–240.

    Google Scholar 

  2. E.S. Golod. On nil-algebras and finitely approximable p-groups (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 28 (1964), 273–276.

    MathSciNet  Google Scholar 

  3. P.S. Novikov, S.I. Adian. On infinite periodic groups. I, II, III (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 32 (1968), 212–244, 251–524, 709–731; (English translation: Math. USSR, Izv., 2 (1968), 209–236, 241–480, 665–685 (1969)).

    MathSciNet  Google Scholar 

  4. J. Levitzki. On the radical of a general ring. Bull. Am. Math. Soc., 49 (1943), 462–466.

    Article  MathSciNet  MATH  Google Scholar 

  5. A.I. Shirshov. On rings with identical relations (in Russian). Mat. Sb., 43 (85), (1957), 277–283.

    MathSciNet  MATH  Google Scholar 

  6. W. Magnus, A connection between the Baker-Hausdorff formula and a problem of Burnside. Ann. Math., 52 (1950), 111–126; 57 (1953), 606.

    Article  MathSciNet  MATH  Google Scholar 

  7. A.I. Kostrikin. On the Burnside problem (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 23 (1959), 3–34.

    MathSciNet  MATH  Google Scholar 

  8. A.I. Kostrikin. Sandwiches in Lie algebras (in Russian). Mat. Sb., 110 (152), (1979), 3–12; (English translation: Math. USSR, Sb., 38 (1981), 1–9).

    MathSciNet  MATH  Google Scholar 

  9. A.I. Kostrikin. Around Burnside (in Russian). "Nauka"; Moscow, 1986.

    Google Scholar 

  10. S.I. Adian, N.N. Repin. Exponential lower estimate for the degree of nilpotency of Engel Lie algebras (in Russian). Mat. Zametki, 39 (1986), 444–452; (English translation: Math. Notes 39 (1986), 244–249).

    MathSciNet  Google Scholar 

  11. Yu.P. Razmyslov. Trace identities of full matrix algebras over a field of characteristic zero (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat., 38 (1974), 723–756. (English translation: Math. USSR, Izv., 8 (1974), 727–760 (1975)).

    MathSciNet  Google Scholar 

  12. H. Zassenhaus. Über Liesche Ringe mit Primzahlcharacteristic. Abh. Math. Semin. Univ. Hamb., 13 (1939), 1–100.

    Article  MathSciNet  Google Scholar 

  13. O. Grün. Zusammenhang zwischen Potenzbildung und Kommutatorbildung. J. Reine Angew. Math., 182 (1940), 158–177.

    MathSciNet  MATH  Google Scholar 

  14. I.N. Sanov. On a system of relations in periodic groups whose exponent is a power of a prime integer (in Russian). Izv. Akad. Nauk SSSR, Ser., Mat., 15 (1951), 477–502.

    MathSciNet  MATH  Google Scholar 

  15. G. Higman. Lie ring methods in the theory of finite nilpotent groups. Proc. Intern. Congr. Math., Edinburgh, 1958, 307–312.

    Google Scholar 

  16. K.A. Ževlakov. Solvability and nilpotency of Jordan rings (in Russian). Algebra Logika, 5 (1966), 37–58.

    Google Scholar 

  17. Ya.S. Dubnov, V.K. Ivanov. On the reduction of degrees of affinor polynomials (in Russian). Dokl. Akad. Nauk SSSR, 41 (1943), 99–102.

    MathSciNet  Google Scholar 

  18. M. Nagata. On the nilpotency of nil algebras. J. Math. Soc. Japan, 4 (1952), 296–301.

    Article  MathSciNet  MATH  Google Scholar 

  19. G. Higman. On a conjecture of Nagata. Math. Proc. Camb. Philos. Soc., 52 (1956), 1–4.

    Article  MathSciNet  MATH  Google Scholar 

  20. E.N. Kuz'min. On a theorem of Nagata-Higman (in Russian). In: Mathematical Structures. Computational mathematics. Mathematical modelling, Bulgarian Academy of Sciences, Sofia, 1975, pp. 101–107.

    Google Scholar 

  21. K.A. Ževlakov, A.M. Slin'ko, I.P. Shestakov, A.I. Shirshov. Rings that are nearly associative (in Russian). "Nauka"; Moscow, (English translation: Academic Press; New York, London, 1982).

    Google Scholar 

  22. A.I. Kostrikin. Lie algebras and finite groups (in Russian). Tr. Mat. Inst. Steklova, 168 (1984), 132–154; (English translation: Proc. Steklov Inst. Math., 168 (1986), 137–159).

    MathSciNet  MATH  Google Scholar 

  23. Yu.P. Razmyslov. On the algebras satisfying the Engel condition (in Russian). Algebra Logika, 10 (1971), 33–44; (English translation: Algebra Logic, 10 (1971), 21–29 (1972)).

    Article  MathSciNet  Google Scholar 

  24. G.V. Dorofeev. An example of a solvable alternative ring which is not nilpotent (in Russian). Usp. Mat. Nauk, 15 (1960), No. 3, 147–150.

    MathSciNet  MATH  Google Scholar 

  25. Dnestrovskaya tetrad': Open problems in ring and module theory (in Russian). Novosibirsk, 1976.

    Google Scholar 

  26. I.P. Shestakov. Radicals and nilpotent elements of free alternative algebras (in Russian). Algebra Logika, 14 (1975), 354–365; (English translation: Algebra Logic, 14 (1975), 219–226 (1976)).

    Article  MATH  Google Scholar 

  27. M. Slater. Prime alternative rings. I, II, III. J. Algebra, 15 (1970), 229–243, 244–251; 21 (1972), (394–409).

    Article  MATH  Google Scholar 

  28. H. Weyl. The classical groups, their invariants and representations. Princeton Univ. Press, Princeton, N.J., 1946.

    MATH  Google Scholar 

  29. A.I. Mal'cev. Algebraic systems (in Russian). "Nauka"; Moscow, 1970; (English translation: Die Grundlehren der mathematischen Wissenschaften, Band 192, Springer-Verlag; Berlin, Heidelberg, New York, 1973).

    Google Scholar 

  30. E.I. Zel'manov. On Lie algebras with the Engel property (in Russian)-Dokl. Akad. Nauk SSSR, 292 (1987), 265–268; (English translation: to appear in Soviet Math. Doklady).

    MathSciNet  Google Scholar 

  31. E.I. Zel'manov. On Jordan nil algebras of bounded degree (in Russian). Varieties of algebraic systems. Preprint No. 647. Computer Center. Novosibirsk, 1986.

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, Siberian Branch of the Academy of Sciences of the USSR, 630090, Novosibirsk, USSR

    E. I. Zel'manov

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  1. E. I. Zel'manov
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Luchezar L. Avramov Kerope B. Tchakerian

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© 1988 Springer-Verlag

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Zel'manov, E.I. (1988). On the nilpotency of nil algebras. In: Avramov, L.L., Tchakerian, K.B. (eds) Algebra Some Current Trends. Lecture Notes in Mathematics, vol 1352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0082029

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  • DOI: https://doi.org/10.1007/BFb0082029

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  • Print ISBN: 978-3-540-50371-2

  • Online ISBN: 978-3-540-45994-1

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