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.
Thesis.-
1. Quadratische Korper im Gebiet der hoheren Kongruenzen I,
II.- Class Field Theory.-
2. Uber die Zetafunktionen gewisser algebraischer
Zahlkorper.-
3. Ober eine neue Art von L-Reihen.-
4. Uber den zweiten
Erganzungssatz zum Reziprozitatsgesetz der l-ten Potenzreste im Korper k? der
l-ten Einheitswurzeln und in Oberkorpern von k?.-
5. Beweis des allgemeinen
Reziprozitatsgesetzes.-
6. Die beiden Erganzungssatze zum Reziprozitatsgesetz
der ln-ten Potenzreste im Korper der ln-ten Einheitswurzeln.-
7. Idealklassen
in Oberkorpern und allgemeines Reziprozitatsgesetz.-
8. Zur Theorie der
L-Reihen mit allgemeinen Gruppencharakteren.- 9 Die gruppentheoretische
Struktur der Diskriminanten algebraischer Zahlkorper.- Algebraic Number
Theory.-
10. Uber Einheiten relativ galoisscher Zahlkorper.-
11. Uber die
Bewertungen algebraischer Zahlkorper.-
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 theorie
des nombres algebriques.-
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 Idele Class Group.- Real Fields.-
18.
Kennzeichnung des Korpers der reellen algebraischen Zahlen.-
19. Algebraische
Konstruktion reeller Korper.-
20. Uber die Zerlegung definiter Funktionen in
Quadrate.-
21. Eine Kennzeichnung der reell abgeschlossenen Korper.- Algebra
and Number Theory.-
22. Die Erhaltung der Kettensatze der Idealtheorie bei
beliebigen endlichen Korpererweiterungen.-
23. Uber einen Satz von Herrn J.
H. Maclagan Wedderburn.-
24. Zur Theorie der hyperkomplexen Zahlen.-
25. Zur
Arithmetik hyperkomplexer Zahlen.-
26. On the Sums of 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
theorie 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 Zopfe.-
35. Zur Isotopic zweidimensionaler Flachen
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 fur
die moderne Mathematik.-
49. Zur Problemlage der Mathematik (lecture
broadcast from RIAS).
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.
