Otto Schilling Explained

Otto Franz Georg Schilling (3 November 1911 – 20 June 1973) was a German-American mathematician known as one of the leading algebraists of his time.^[1]

He was born in Apolda and studied in the 1930s at the Universität Jena and the Universität Göttingen under Emmy Noether. After Noether was forced to leave Germany by the Nazis, he found a new advisor in Helmut Hasse,^[2] and obtained his Ph.D. from Marburg University in 1934 on the thesis Über gewisse Beziehungen zwischen der Arithmetik hyperkomplexer Zahlsysteme und algebraischer Zahlkörper. He then was post doc at Trinity College, Cambridge before moving to Institute for Advanced Study 1935–37^[3] and the Johns Hopkins University 1937–39. He became an instructor with the University of Chicago in 1939,^[2] promoted to assistant professor 1943, associate 1945 and full professor in 1958. In 1961 he moved to Purdue University. He died in Highland Park, Illinois. His students were, among others, the game theorist Anatol Rapoport and the mathematician Harley Flanders.

Articles

Arithmetic in a Special Class of Algebras. The Annals of Mathematics. 38. 1. 1937. 116–119. 0003-486X. 10.2307/1968513. 1968513. Schilling. Otto F. G..
Class Fields of Infinite Degree Over p-Adic Number Fields. The Annals of Mathematics. 38. 2. 1937. 469–476. 0003-486X. 10.2307/1968563. 1968563. Schilling. Otto F. G..
Arithmetic in Fields of Formal Power Series in Several Variables. The Annals of Mathematics. 38. 3. 1937. 551–576. 0003-486X. 10.2307/1968600. 1968600. Schilling. O. E. G.. (typo in Schilling's name)
The Structure of Local Class Field Theory. American Journal of Mathematics. 60. 1. 1938. 75–100. 0002-9327. 10.2307/2371544. 2371544. Schilling. O. F. G..
A Generalization of Local Class Field Theory. American Journal of Mathematics. 60. 3. 1938. 667–704. 0002-9327. 10.2307/2371605. 2371605. Schilling. O. F. G..
Units in p-Adic Algebras. American Journal of Mathematics. 61. 4. 1939. 883–896. 0002-9327. 10.2307/2371632. 2371632. Schilling. O. F. G..
with Saunders Mac Lane: Zero-Dimensional Branches of Rank One on Algebraic Varieties. The Annals of Mathematics. 40. 3. 1939. 507–520. 0003-486X. 10.2307/1968935. 1968935. MacLane. Saunders. Schilling. O. F. G..
with Saunders Mac Lane: Infinite Number Fields with Noether Ideal Theories. American Journal of Mathematics. 61. 3. 1939. 771–782. 0002-9327. 10.2307/2371335. 2371335. Lane. Saunders Mac. Schilling. O. F. G..
with Saunders Mac Lane: Normal Algebraic Number Fields. Proceedings of the National Academy of Sciences. 26. 2. 1940. 122–126. 0027-8424. 10.1073/pnas.26.2.122. free. MacLane. S.. Schilling. O. F. G.. 16588322. 1078017.
Regular normal extensions over complete fields. Trans. Amer. Math. Soc.. 1940. 47. 3. 440–454. 0001970. 10.1090/s0002-9947-1940-0001970-2. free. Schilling. O. F. G..
Remarks on a Special Class of Algebras. American Journal of Mathematics. 62. 1/4. 1940. 346–352. 0002-9327. 10.2307/2371458. 2371458. Schilling. O. F. G..
with Saunders Mac Lane: A formula for the direct products of crossed product algebras. Bull. Amer. Math. Soc.. 1942. 48. 2. 108–114. 0006152. 10.1090/s0002-9904-1942-07613-0. free. MacLane. Saunders. Schilling. O. F. G..
with Irving Kaplansky: Some remarks on relatively complete fields. Bulletin of the American Mathematical Society. 48. 10. 1942. 744–748. 0002-9904. 10.1090/S0002-9904-1942-07772-X. free. Kaplansky. Irving. Schilling. O. F. G..
Normal Extensions of Relatively Complete Fields. American Journal of Mathematics. 65. 2. 1943. 309–334. 0002-9327. 10.2307/2371818. 2371818. Schilling. O. F. G..
On a special class of abelian functions. Bull. Amer. Math. Soc.. 1945. 51. 2. 133–136. 0011291. 10.1090/s0002-9904-1945-08293-7. free. Schilling. O. F. G..
Noncommutative valuations. Bull. Amer. Math. Soc.. 1945. 51. 4. 297–304. 0011684. 10.1090/s0002-9904-1945-08339-6. free. Schilling. O. F. G..
Ideal theory on open Riemann surfaces. Bull. Amer. Math. Soc.. 1946. 52. 11, Part 1. 945–963. 0019733. 10.1090/s0002-9904-1946-08669-3. free. Schilling. O. F. G..
Mathematical Journal of Okayama University. 0030-1566. 3. 1. 5–10. 1953. Necessary conditions for local class field theory.
On local class field theory. Journal of the Mathematical Society of Japan. 13. 3. 1961. 234–245. 0025-5645. 10.2969/jmsj/01330234. free. f. g. Schilling. O..

Books

Book: Schilling, Otto. Theory of Valuations. 1950. American Mathematical Society. 0821815040. ^[4]
Book: Basic abstract algebra. Otto. Schilling. William Stephen. Piper. 1975. Allyn & Bacon. 0205042732.

(394 pages)

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Notes and References

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Web site: Otto Franz Georg Schilling. Institute for Advanced Study. 9 December 2019.
Hochschild, G.. Gerhard Hochschild. Review: The theory of valuations, by O. F. G. Schilling. Bull. Amer. Math. Soc.. 1951. 57. 1, Part 1. 91–94. 10.1090/s0002-9904-1951-09464-1. free.