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Constructions of Special Radicals of Algebras

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This paper is devoted to the discussion of some schemes of construction of radicals similar to special radicals, which generalize constructions of the basic special radicals of the algebras close to associative ones.

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References

  1. V. A. Andrunakievich, “Radicals of associative rings. I,” Mat. Sb., 44 (86), 179–212 (1958).

    MathSciNet  MATH  Google Scholar 

  2. V. A. Andrunakievich and V. M. Ryabukhin, Radicals of Algebras and Structure Theory [in Russian], Nauka, Moscow (1979).

    MATH  Google Scholar 

  3. A. M. Babich, “On Levitzki radical,” Dokl. Akad. Nauk SSSR, 126, 242–243 (1959).

    MathSciNet  MATH  Google Scholar 

  4. G. V. Dorofeev, “On a locally nilpotent radical of non-associative rings,” Algebra Logika, 10, No. 4, 355–364 (1971).

    Article  MathSciNet  Google Scholar 

  5. E. García and M. Gómez Lozano, “A characterization of the Kostrikin radical of a Lie algebra,” J. Algebra, 346, 266–283 (2011).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. G. Kurosh, “Non-associative free algebras and free products of algebras,” Mat. Sb., 20 (62), No. 2, 239–262 (1947).

    MathSciNet  MATH  Google Scholar 

  7. V. N. Latyshev, A. V. Mikhalev, and S. A. Pikhtil’kov, “On the sum of locally solvable ideals of Lie algebras,” Vestn. Mosk. Univ. Ser. 1 Mat. Mekh., No. 3, 29–32 (2003).

  8. V. A. Parfenov, “On the weakly solvable radical of Lie algebras,” Sib. Mat. Zh., 12, No. 1, 171–176 (1971).

    Article  MathSciNet  MATH  Google Scholar 

  9. L. H. Rowen, Polynomial Identities in Ring Theory, Pure Appl. Math., Vol. 84, Academic Press, London (1980).

  10. K. K. Schukin, “On the locally solvable radical of one class of groups,” Uchen. Zap. Kishinev. Univ., No. 54, 95–100 (1960).

  11. V. G. Skosyrskii, Radicals of Jordan Algebras and Associative Algebras Connected with Them, Ph.D. Thesis, Novosibirsk (1981).

  12. A. Thedy, “Radicals of right-alternative and Jordan rings,” Commun. Algebra, 12, No. 7, 857–887 (1984).

    Article  MathSciNet  MATH  Google Scholar 

  13. A. Thedy, “Z-closed ideals of quadratic Jordan algebras,” Commun. Algebra, 13, No. 12, 2537–2565 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  14. E. I. Zel’manov, “Characterization of the McCrimmon radical,” Sib. Mat. Zh., 25, No. 5, 190–192 (1984).

    MathSciNet  MATH  Google Scholar 

  15. K. A. Zhevlakov and I. P. Shestakov, “On local finiteness in the sense of Shirshov,” Algebra Logika, 12, No. 1, 41–73 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  16. K. A. Zhevlakov, A. M. Slin’ko, I. P. Shestakov, and A. I. Shirshov, Rings That Are Nearly Associative, Academic Press, New York (1982).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Bauman Moscow State Technical University, Moscow, Russia

    A. Yu. Golubkov

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  1. A. Yu. Golubkov
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Correspondence to A. Yu. Golubkov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 1, pp. 57–133, 2015.

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Golubkov, A.Y. Constructions of Special Radicals of Algebras. J Math Sci 223, 530–580 (2017). https://doi.org/10.1007/s10958-017-3366-8

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  • DOI: https://doi.org/10.1007/s10958-017-3366-8

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