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Siberian Mathematical Journal

, Volume 28, Issue 6, pp 899–906 | Cite as

Goldie's theorems for Jordan algebras

  • E. I. Zel'manov
Article

Keywords

Jordan Algebra 
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Literature Cited

  1. 1.
    N. Jacobson, “Structure theory for a class of Jordan algebras,” Proc. Nat. Acad. Sci. USA,55, No. 1, 243–251 (1966).Google Scholar
  2. 2.
    K. McCrimmon, “A general theory of Jordan rings,” Proc. Nat. Acad. Sci. USA,56, No. 4, 1072–1079 (1966).Google Scholar
  3. 3.
    A. W. Goldie, “Semiprime rings with maximum conditions,” Proc. London Math. Soc.,10, No. 2, 201–220 (1960).Google Scholar
  4. 4.
    E. I. Zel'manov, “Jordan algebras with finiteness conditions,” Algebra Logika,17, No. 6, 693–704 (1978).Google Scholar
  5. 5.
    N. Jacobson, K. McCrimmon and M. Parvathi, “Localization in Jordan algebras,” Commun. Algebra,6, No. 9, 911–958 (1978).Google Scholar
  6. 6.
    D. J. Britten, “On semiprime Jordan rings H(R) with ACC,” Proc. Am. Math. Soc.,45, No. 2, 175–178 (1974).Google Scholar
  7. 7.
    D. J. Britten, “On prime Goldielike quadratic Jordan matrix algebras,” Can. Math. Bull.,20, No. 1, 39–45 (1977).Google Scholar
  8. 8.
    K. A. Zhevlakov, A. M. Slin'ko, I. P. Shestakov, and A. I. Shirshov, Near Associative Rings [in Russian], Nauka, Moscow (1978).Google Scholar
  9. 9.
    N. Jacobson, Structure and Representations of Jordan Algebras, AMS, Providence, R. I. (1969).Google Scholar
  10. 10.
    K. McCrimmon, “The radical of a Jordan algebra,” Proc. Nat. Acad. Sci. U.S.A.,62, No. 4, 671–678 (1969).Google Scholar
  11. 11.
    S. A. Amitsur, “Algebras over infinite fields,” Proc. Am. Math. Soc.,7, No. 2, 355–361 (1956).Google Scholar
  12. 12.
    K. McCrimmon, “A characterization of the radical of Jordan algebra,” J. Algebra,18, No. 1, 103–111 (1971).Google Scholar
  13. 13.
    A. I. Mal'tsev, Algebraic Systems [in Russian], Nauka, Moscow (1975).Google Scholar
  14. 14.
    A. Levitzki, “A problem of A. Kurosh,” Bull. Am. Math. Soc.,52, No. 6, 1033–1035 (1946).Google Scholar
  15. 15.
    A. V. Chekhonadskikh, “Nil-ideals of Jordan triple systems with finiteness conditions,” Sib. Mat. Zh.,26, No. 1, 159–169 (1985).Google Scholar
  16. 16.
    E. I. Zel'manov, “On prime Jordan algebras. II,” Sib. Mat. Zh.,24, No. 1, 89–104 (1983).Google Scholar
  17. 17.
    J. Lambek, Rings and Modules [Russian translation], Mir, Moscow (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • E. I. Zel'manov

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