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Galois objects and extensions of Hopf Algebras

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Category Theory, Homology Theory and their Applications II

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REF

  1. Artin, E., and Tate, J., Class Field Theory, Princeton University mimeographed notes, Princeton, New Jersey (1960).

    MATH  Google Scholar 

  2. Artin, M., Grothendieck Topologies, Harvard University mimeographed notes, Cambridge, Massachusetts (1962).

    Google Scholar 

  3. Bourbaki, N., Algébre Commutative, Chapters I–II, Hermann, Paris (1962).

    Google Scholar 

  4. Chase, S. U., Harrison, D. K., and Rosenberg, Alex, “Galois Theory and Galois Cohomology of Commutative Rings,” Memoirs Amer. Math. Soc., Vol. 52; 15–33, (1965).

    MathSciNet  MATH  Google Scholar 

  5. Chase, S. U., and Rosenberg, Alex, “Amitsur Cohomology and the Brauer Group,” Memoirs Amer. Math. Soc., Vol. 52; 34–79, (1965).

    MathSciNet  MATH  Google Scholar 

  6. Chase, S. U., and Rosenberg, Alex, “A Theorem of Harrison, Kummer Theory, and Galois Algebras,” Nagoya Math. J., Vol. 27; 663–685, (1966).

    Article  MathSciNet  MATH  Google Scholar 

  7. Chase, S. U., “Abelian Extensions and a Cohomology Theory of Harrison,” 375–403 in Proceedings of the Conference on Categorical Algebra, La Jolla (1965), Springer-Verlag, New York Inc., (1966).

    Google Scholar 

  8. Epp, H. P., Commutative Group Schemes, Harrison's Theorem, and Galois Extensions, Ph.D. thesis, Northwestern University, (1966).

    Google Scholar 

  9. Giraud, J., Cohomologie Non-Abelienne, Columbia University Notes (1965).

    Google Scholar 

  10. Harrison, D. K., “Abelian Extensions of Arbitrary Fields,” Trans. Amer. Math. Soc., Vol. 106; 230–235, (1963).

    Article  MathSciNet  MATH  Google Scholar 

  11. -, “Abelian Extensions of Commutative Rings,” Memoirs Amer. Math. Soc., 52; 1–14, (1965).

    MathSciNet  MATH  Google Scholar 

  12. Hasse, H., “Invariante Kennzeichnung Galoisscher Körper mit Vorgegebener Galoisgruppe,” J. Reine Angew. Math., vol. 187; 14–43, (1950).

    MathSciNet  MATH  Google Scholar 

  13. MacClane, S., Homology, Academic Press, New York, (1963).

    Book  Google Scholar 

  14. Oort, F., Commutative Group Schemes, (Lecture Notes in Mathematics, vol. 15), Springer-Verlag, Berlin, (1966).

    MATH  Google Scholar 

  15. Orzech, M., “A Cohomology Theory for Commutative Galois Extensions,” Math. Zeitschr., vol. 105; 128–140, (1968).

    Article  MathSciNet  MATH  Google Scholar 

  16. Orzech, M., “A Cohomological Description of Abelian Galois Extensions,” to appear.

    Google Scholar 

  17. Shatz, S., “Cohomology of Artinian Group Schemes Over Local Fields,” Ann. of Math., Vol. 79; 411–449, (1964).

    Article  MathSciNet  MATH  Google Scholar 

  18. Serre, J. P., Groupes Algebriques et Corps de Classes, Hermann, Paris, (1959), (Act. Sci. Ind. #1264).

    MATH  Google Scholar 

  19. —, Corps Locaux, Hermann, Paris, (1962), (Act. Sci. Ind. #1296).

    MATH  Google Scholar 

  20. Strasbourg University Department of Mathematics, “Groupes Algebriques,” Seminaire Heidelberg-Strasbourg Annee 1965–66.

    Google Scholar 

  21. Sweedler, M. E., “The Hopf Algebra of an Algebra as Applied to Field Theory,” J. of Algebra, Vol. 8; 262–276, (1968).

    Article  MathSciNet  MATH  Google Scholar 

  22. -, “Structure of Inseparable Extensions,” Annals of Math., Vol. 87; 401–410, (1968).

    Article  MathSciNet  MATH  Google Scholar 

  23. Wolf, P., “Algebraische Theorie der Galoisschen Algebren,” Deutscher Verlag der Wissenschaften, Math. Forschungsberichte III, Berlin, (1956). *** DIRECT SUPPORT *** A00J4082 00002

    Google Scholar 

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Chase, S.U. (1969). Galois objects and extensions of Hopf Algebras. In: Category Theory, Homology Theory and their Applications II. Lecture Notes in Mathematics, vol 92. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080763

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  • DOI: https://doi.org/10.1007/BFb0080763

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04611-0

  • Online ISBN: 978-3-540-36101-5

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