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On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras

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References

  1. Speiser, A.: Zahlentheoretische Sätze aus der Gruppentheorie. Math. Z. 5 (1919), Satz 1. A similar proof, valid for the group of regular elements of an arbitrary algebra, was given byKolchin andLang, Existence of invariant bases, Proceedings Amer. Math. Soc.11 (1960), proposition 2.

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  2. Schur, I.: Einige Bemerkungen zu der vorstehenden Arbeit von Herrn A.Speiser. Math. Z.5 (1919), Satz II.

  3. For this theory we refer tov. d. Waerden's Algebra II (4th edition), chap. 17–18.

  4. Chatelet: Variations sur une thème de Poincaré. Ann. Ecole Norm. (3)59, 249–300 (1944).

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  5. Witt, E.: Über ein Gegenbeispiel zum Normensatz. Math. Z.39, 462–467 (1934).

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  6. Amitsur: Generic splitting fields of central simple algebras. Ann. Math.62, 8–43 (1955).

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  7. For the theory of places see e.g.Zariski-Samuel, Commutative Algebra II (Princeton 1960), chap. VI.

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  1. Tübingen

    Peter Roquette

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  1. Peter Roquette
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Dedicated toBarthel v. d. Waerden on his 60th birthday

This work was supported in part by a grant of the National Science Foundation while the author was visiting the University of Notre Dame and the California Institute of Technology.

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Roquette, P. On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras. Math. Ann. 150, 411–439 (1963). https://doi.org/10.1007/BF01357435

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