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Centralizer theorems for Hopf type Galois extensions

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References

  1. Auslander, M., Goldman, O.: Maximal orders. Trans. Amer. Math. Soc.97, 1–24 (1960)

    Google Scholar 

  2. Auslander, M., Goldman, O.: The Brauer group of a commutative ring. Trans. Amer. Math. Soc.97, 367–409 (1960)

    Google Scholar 

  3. Azumaya, G.: Completely faithful modules and self injective rings. Nagoya Math. J.27, 697–708 (1966)

    Google Scholar 

  4. Bourbaki, N.: Algebre Commutative. Paris: Hermann 1961

    Google Scholar 

  5. Chase, S.U., Harrison, D.K., Rosenberg, A.: Galois theory and Galois cohomology of commutative rings. Mem. Amer. Math. Soc.52, 15–33 (1965)

    Google Scholar 

  6. Chase, A.U., Sweedler, M.E.: Hopf algebras and Galois theory. Lecture Notes in Math.97. Berlin-Heidelberg-New York: Springer 1969

    Google Scholar 

  7. DeMeyer, F.R.: Some notes on the general Galois theory of rings. Osaka J. Math.2, 117–127 (1965)

    Google Scholar 

  8. Endo, S.: Completely faithful modules and quasi-Frobenius algebras. J. Math. Soc. Japan19, 437–456 (1967)

    Google Scholar 

  9. Hattori, A.: Semisimple algebras over a commutative ring. J. Math. Soc. Japan15, 404–419 (1963)

    Google Scholar 

  10. Hirata, K., Sugano, K.: On semisimple extensions and separable extensions over non-commutative rings. J. Math. Soc. Japan18, 360–373 (1966)

    Google Scholar 

  11. Hirata, K.: Some types of separable extensions of rings. Nagoya Math. J.33, 107–115 (1968)

    Google Scholar 

  12. Hirata, K.: Separable extensions and centralizers of rings. Nagoya Math. J.35, 31–45 (1969)

    Google Scholar 

  13. Hochschild, G.: Note on relative homological algebra. Trans. Amer. Math. Soc.82, 246–269 (1956)

    Google Scholar 

  14. Kanzaki, T.: On commutor rings and Galois theory of separable algebras. Osaka J. Math.2, 137–145 (1965)

    Google Scholar 

  15. Kanzaki, T.: On generalized crossed product and Brauer group. Osaka. J. Math.5, 175–188 (1968)

    Google Scholar 

  16. Kasch, F.: Projective Frobenius-Erweiterungen. Sitzungsber. Heidelb. Akad. Wiss. Math.-Natur. Kl. 1960/1961, 89–109

  17. Kreimer, H.F., Takeuchi, M.: Hopf algebras and Galois extensions of an algebra. Indiana Univ. Math. J.30, 675–692 (1981)

    Google Scholar 

  18. Larson, R.G., Sweedler, M.E.: An associative orthogonal bilinear form for Hopf algebras. Amer. J. Math.91, 75–94 (1967)

    Google Scholar 

  19. Miyashita, Y.: Finite outer Galois theory of non-commutative rings. J. Fac. Sci. Hokkaido Univ. Ser. I19, 114–134 (1966)

    Google Scholar 

  20. Miyashita, Y.: On Galois extensions and crossed products. J. Fac. Sci. Hokkaido Univ. Ser. I21, 97–121 (1970)

    Google Scholar 

  21. Morita, K.: Duality for modules and its application to the theory of rings with minimum condition. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A6, 83–142 (1958)

    Google Scholar 

  22. Morita, K.: Adjoint pairs of functors and Frobenius extensions. Sci. Rep. Tokyo Kyoiku Daigaku Sect. A9, 40–71 (1965)

    Google Scholar 

  23. Morita, K.: The endomorphism ring theorem for Frobenius extensions. Math. Z.102, 385–404 (1967)

    Google Scholar 

  24. Müller, B.: Quasi-Frobenius Erweiterungen. Math. Z.85, 345–368 (1964)

    Google Scholar 

  25. Nakayama, T.: On a generalized notion of Galois extensions of a ring. Osaka J. Math.15, 11–13 (1963)

    Google Scholar 

  26. Pareigis, B.: When Hopf algebras are Frobenius algebras. J. Algebra18, 588–596 (1971)

    Google Scholar 

  27. Sugano, K.: Note on semi-simple extensions and separable extensions. Osaka J. Math.4, 265–270 (1967)

    Google Scholar 

  28. Sweedler, M.E.: Hopf algebras. New York: Benjamin 1969

    Google Scholar 

  29. Ulbrich, K.H.: Vollgraduierte Algebren. Abh. Math. Sem. Univ. Hamburg51, 136–148 (1981)

    Google Scholar 

  30. Ulbrich, K.H.: Galoiserweiterungen von nicht-kommutativen Ringen. Comm. Algebra10(6), 655–672 (1982)

    Google Scholar 

  31. Yokogawa, K.: OnSR S-module structure ofS/R-Azumaya algebras. Osaka J. Math.12, 673–690 (1975)

    Google Scholar 

  32. Yokogawa, K.: Non-commutative Hopf Galois extensions. Osaka J. Math.18, 63–73 (1981)

    Google Scholar 

  33. Yokagawa, K.: A pair of subalgebras in an Azumaya algebra. To appear in Osaka J. Math.

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Miyashita, Y. Centralizer theorems for Hopf type Galois extensions. Math Z 187, 125–144 (1984). https://doi.org/10.1007/BF01163172

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  • DOI: https://doi.org/10.1007/BF01163172

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