Geodesic
Simple Algebras Over Rational Function Fields
Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 831-835

Voir la notice de l'article provenant de la source Cambridge University Press

The well-known Hasse-Brauer-Noether theorem states that a simple algebra with center a number field k splits over k (i.e., is a full matrix algebra) if and only if it splits over the completion of k at every rank one valuation of k. It is natural to ask whether this principle can be extended to a broader class of fields. In particular, we prove here the following extension. 
Nyman, T.; Whaples, G. Simple Algebras Over Rational Function Fields. Canadian journal of mathematics, Tome 31 (1979) no. 4, pp. 831-835. doi: 10.4153/CJM-1979-078-1
@article{10_4153_CJM_1979_078_1,
     author = {Nyman, T. and Whaples, G.},
     title = {Simple {Algebras} {Over} {Rational} {Function} {Fields}},
     journal = {Canadian journal of mathematics},
     pages = {831--835},
     year = {1979},
     volume = {31},
     number = {4},
     doi = {10.4153/CJM-1979-078-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-078-1/}
}
TY  - JOUR
AU  - Nyman, T.
AU  - Whaples, G.
TI  - Simple Algebras Over Rational Function Fields
JO  - Canadian journal of mathematics
PY  - 1979
SP  - 831
EP  - 835
VL  - 31
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-078-1/
DO  - 10.4153/CJM-1979-078-1
ID  - 10_4153_CJM_1979_078_1
ER  - 
%0 Journal Article
%A Nyman, T.
%A Whaples, G.
%T Simple Algebras Over Rational Function Fields
%J Canadian journal of mathematics
%D 1979
%P 831-835
%V 31
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-078-1/
%R 10.4153/CJM-1979-078-1
%F 10_4153_CJM_1979_078_1

[1] 1. Albert, A. A., Structure of algebras (A.M.S. Colloquium Publication XXIV, New York, 1939). Google Scholar

[2] 2. Artin, E., Algebraic numbers and algebraic functions (New York University and Princeton University, 1951; Gordon and Breach, 1967). Google Scholar

[3] 3. Auslander, M. and Brumer, A., Brauer groups of discrete valuation rings, Indag. Math. 30 (1968), 286–296. Google Scholar

[4] 4. Faddeev, D. K., Simple algebras over afield of algebraic functions of one variable, Trudy Mat. Inst. Steklov 38 (1951), 321-344, A.M.S. Translat. Ser. I. 3 (1956), 15–38. Google Scholar

[5] 5. Jacobson, Nathan, P-Algebras of exponent p, Bull. A.M.S. 43 (1937), 667–670. Google Scholar

[6] 6. Nyman, T. and Whaples, G., Hasse's principle for simple algebras over function fields of curves. I. Algebras of index 2 and 3; curves of genus 0 and 1, J. reine angew. Math. 299/300 (1978), 396–405. Google Scholar

[7] 7. Tsen, C. C., Divisionalgebren uber Funktionenkorpern, Gott. Nachr. (1933), 335–339. Google Scholar

[8] 8. Witt, E., Der Existenzsatz fur abelsche Funktionenkorper, J. reine angew. Math. 173 (1935), 43–51. Google Scholar

Cité par Sources :