Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T06:54:07.542Z Has data issue: false hasContentIssue false
  • English
  • Français

Splitting of Algebras by Function Fields of One Variable

Published online by Cambridge University Press:  22 January 2016

Peter Roquette
Peter Roquette*
Affiliation:
Tübingen University, Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let K be a field and (K) the Brauer group of K. It consists of the similarity classes of finite central simple algebras over K. For any field extension F/K there is a natural mapping (K) → (F) which is obtained by assigning to each central simple algebra A/K the tensor product which is a central simple algebra over F. The kernel of this map is the relative Brauer group (F/K), consisting of those A ∈(K) which are split by F.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 27 , Issue 2 , July 1966 , pp. 625 - 642
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Artin, , Kohomologietheorie endlicher Gruppen; Vorlesungsausarbeitung Hamburg, (1957).Google Scholar
[2] Artin-Nesbitt-Thrall, , Rings with minimum condition, Ann Arbor (1944).Google Scholar
[3] Cartan-Eilenberg, , Homological Algebra, Princeton, (1956).Google Scholar
[4] Cassels, , Arithmetic on Curves of genus one. VI. The Tate-Šafarevič group can be arbitrarily large, Journal für die reine und angewandte Mathematik, vol. 214/215 (1964), 65–70.CrossRefGoogle Scholar
[5] Chevalley, , Introduction to the theory of functions of one variable, New York, (1951).Google Scholar
[6] Deuring, , Algebren, Berlin, (1935).CrossRefGoogle Scholar
[7] Hasse, , Zum Existenzsatz von Grunwald in der Klassenkörpertheorie, Journal für die reine und angewandte Mathematik, vol. 188 (1950), 40–64.Google Scholar
[8] Reichardt, , Einige im Kleinen überall lösbare, im Grossen unlösbare diophantische Gleichungen; Journal für die reine und angewandte Mathematik vol. 184 (1942), 12–18.Google Scholar
[9] Roquette, , On the Galois cohomology of the projective linear group and its applications to the construction of generic splitting fields of algebras; Mathematisches Annalen, vol. 150 (1963), 411–439.Google Scholar
[10] Serre, , Corps locaux, Paris, (1962).Google Scholar
[11] Tate, , WC-groups over p-adic fields; Séminaire Bourbaki no. 156, Paris, (1957).Google Scholar
[12] Witt, , Zerlegung reeller algebraischer Funktionen in Quadrate. Schiefkörper über reellem Funktionenkorper. Journal fur die reine und angewandte Mathematik, vol. 171 (1934), 4–11.Google Scholar
[13] Witt, , Über ein Gegenbeispiel zum Normensatz, Mathematische Zeitschrift, vol. 39 (1935), 492–467.Google Scholar
[14] Witt, , Schiefkorper über diskret bewerteten Körpern. Journal fur die reine und angewandte Mathematik, vol. 176 (1937), 153–156.Google Scholar
[15] Zariski-Samuel, , Commutative Algebra, vol. II, Princeton, (1960).Google Scholar