Collected Papers - Artin, Emil

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Résumé :
Emil Artin was one of the leading algebraists of the 20th century. He worked in algebraic number theory, contributing largely to class field theory and a new construction of L-functions. He also contributed to the pure theories of rings, groups and fields. Artin developed the theory of braids as a branch of algebraic topology. He was also an important expositor of Galois theory, and of the group cohomology approach to the class ring theory (with John Tate), just to mention two theories where his formulations have became an established standard. The influential treatment of abstract algebra by van der Waerden is said to derive in part from Artin's ideas, as do those by Emmy Noether. This volume is a reprint of Artin's works.

Biographie:
Emil Artin was born in Vienna in 1898. He studied under G. Herglotz and got his PhD at the University of Leizpig in 1921. In July 1923, Artin obtained the Venia legendi for mathematics at Hamburg University and was appointed Extraordinarius in 1925 and Ordinarius in 1926, at the age of 28. For eleven years, Artin directed the activities of the Mathematical Seminar of Hamburg University together with Hecke and Blaschkethe. In fall 1937, Artin emigrated to the United States of America with his wife and family, where he taught at Notre Dame University for a year, thereafter at Indiana University, Bloomington, from 1938 until 1946 and finally at Princeton University from 1946 until 1958. Starting in fall 1958, he taught at Hamburg University again. In 1962, he died in Hamburg....

Sommaire:
Thesis.- 1. Quadratische K?rper im Gebiet der h?heren Kongruenzen I, II.- Class Field Theory.- 2. ?ber die Zetafunktionen gewisser algebraischer Zahlk?rper.- 3. Ober eine neue Art von L-Reihen.- 4. ?ber den zweiten Erg?nzungssatz zum Reziprozit?tsgesetz der l-ten Potenzreste im K?rper k? der l-ten Einheitswurzeln und in Oberk?rpern von k?.- 5. Beweis des allgemeinen Reziprozit?tsgesetzes.- 6. Die beiden Erg?nzungss?tze zum Reziprozit?tsgesetz der ln-ten Potenzreste im K?rper der ln-ten Einheitswurzeln.- 7. Idealklassen in Oberk?rpern und allgemeines Reziprozit?tsgesetz.- 8. Zur Theorie der L-Reihen mit allgemeinen Gruppencharakteren.- 9 Die gruppentheoretische Struktur der Diskriminanten algebraischer Zahlk?rper.- Algebraic Number Theory.- 10. ?ber Einheiten relativ galoisscher Zahlk?rper.- 11. ?ber die Bewertungen algebraischer Zahlk?rper.- 12. Axiomatic Characterization of Fields by the Product Formula for Valuations.- 13. A Note on Axiomatic Characterization of Fields.- 14. Questions de base minimale dans la th?orie des nombres alg?briques.- 15. The Class-Number of Real Quadratic Fields.- 16. The Class-Number of Real Quadratic Number Fields.- 17. Representatives of the Connected Component of the Id?le Class Group.- Real Fields.- 18. Kennzeichnung des K?rpers der reellen algebraischen Zahlen.- 19. Algebraische Konstruktion reeller K?rper.- 20. ?ber die Zerlegung definiter Funktionen in Quadrate.- 21. Eine Kennzeichnung der reell abgeschlossenen K?rper.- Algebra and Number Theory.- 22. Die Erhaltung der Kettens?tze der Idealtheorie bei beliebigen endlichen K?rpererweiterungen.- 23. ?ber einen Satz von Herrn J. H. Maclagan Wedderburn.- 24. Zur Theorie der hyperkomplexen Zahlen.- 25. Zur Arithmetik hyperkomplexer Zahlen.- 26. On the Sumsof Two Sets of Integers.- 27. The Theory of Simple Rings.- 28. The Free Product of Groups.- 29. Linear Mappings and the Existence of a Normal Basis.- 30. Remarques concernant la th?orie de Galois.- 31. A Note on Finite Ring Extensions.- 32. The Orders of the Linear Groups.- 33. The Orders of the Classical Simple Groups.- Topology.- 34. Theorie der Z?pfe.- 35. Zur Isotopic zweidimensionaler Fl?chen im R4.- 36. Theory of Braids.- 37. Braids and Permutations.- 38. Some Wild Cells and Spheres in Three-Dimensional Space.- 39. The Theory of Braids.- Miscellaneous.- 40. Ein mechanisches System mit quasiergodischen Bahnen.- 41. Coordinates in Affine Geometry.- 42. On the Independence of Line Integrals on the Path.- 43. On the Theory of Complex Functions.- 44. A Proof of the Krein-Milman Theorem.- General.- 45. The Influence of J. H. M. Wedderburn on the Development of Modern Algebra.- 46. Review of Bourbaki's Algebra.- 47. Contents and Methods of an Algebra Course.- 48. Die Bedeutung Hilberts f?r die moderne Mathematik.- 49. Zur Problemlage der Mathematik (lecture broadcast from RIAS)....