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Cyclic division algebras

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An Erratum to this article was published on 01 September 1982

Abstract

A general example of cyclic division algebra is given, based on a construction of Brauer, yielding examples of division algebras of arbitrary prime exponent without proper central subalgebras, and also noncrossed products of arbitrary exponent.

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References

  1. A. A. Albert,Modern Higher Algebra, University of Chicago Press, Chicago, Illinois, 1937.

    Google Scholar 

  2. A. A. Albert,Structure of Algebras, Amer. Math. Soc. Colloq. Pub. 24, Providence, R.I., 1961.

  3. S. A. Amitsur,On central division algebras, Israel J. Math.12 (1972), 408–422.

    Article  MATH  MathSciNet  Google Scholar 

  4. S. A. Amitsur and D. Saltman,Generic abelian crossed products, J. Algebra51 (1978), 76–87.

    Article  MATH  MathSciNet  Google Scholar 

  5. S. A. Amitsur, L. H. Rowen and J. P. Tignol,Division algebras of degree 4 and 8 with involution, Israel J. Math.33 (1979), 133–148.

    Article  MATH  MathSciNet  Google Scholar 

  6. R. Brauer,Uber den index und den exponenten von divisionsalgebren, Tohuko Math. J.37 (1933), 77–87.

    MATH  Google Scholar 

  7. A. Charnow,On the fixed field of a linear abelian group, J. London Math. Soc. (2),1 (1969), 348–350.

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Jacobson,PI-algebras, an Introduction, Lecture Notes in Mathematics441, Springer Verlag, Berlin-Heidelberg-New York, 1975.

    MATH  Google Scholar 

  9. L. Risman,Cyclic algebras, complete fields, and crossed products, Israel J. Math.28 (1977), 113–128.

    Article  MATH  MathSciNet  Google Scholar 

  10. L. Rowen,On algebras with polynomial identity, Dissertation, Yale University, 1973.

  11. L. Rowen,Identities in algebra with involution, Israel J. Math.20 (1975), 70–95.

    Article  MATH  MathSciNet  Google Scholar 

  12. L. Rowen,Central simple algebras, Israel J. Math.29 (1978), 285–301.

    MATH  MathSciNet  Google Scholar 

  13. L. Rowen,Polynomial Identities in Ring Theory, Academic Press, New York, 1980.

    MATH  Google Scholar 

  14. L. Rowen,Division algebra counterexamples of degree 8, israel J. Math.38 (1981), 51–57.

    MATH  MathSciNet  Google Scholar 

  15. D. Saltman,Noncrossed products of small exponent, Proc. Amer. Math. Soc.68 (1978), 165–168.

    Article  MATH  MathSciNet  Google Scholar 

  16. D. Saltman,Indecomposible division algebras, Comm. Alg.7 (1979), 791–817.

    Article  MATH  MathSciNet  Google Scholar 

  17. H. M. S. Wedderburn,On division algebras, Trans. Amer. Math. Soc.22 (1921), 129–135.

    Article  MathSciNet  Google Scholar 

  18. D. Winter,The Structure of Fields, Springer-Verlag, New York, Berlin, 1974.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Bar Ilan University, Ramat Gan, Israel

    Louis Halle Rowen

Authors
  1. Louis Halle Rowen
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Additional information

This research was supported in part by the U.S.-Israel Binational Science Foundation.

An erratum to this article is available at http://dx.doi.org/10.1007/BF02761948.

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Rowen, L.H. Cyclic division algebras. Israel J. Math. 41, 213–234 (1982). https://doi.org/10.1007/BF02771722

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  • DOI: https://doi.org/10.1007/BF02771722

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