Alex Rosenberg

Alex FTW Rosenberg (born December 5, 1926 in Berlin , † October 27, 2007 in Schwerte ) was an American mathematician who studied algebra .

life and work

In 1939, Rosenberg emigrated with his parents and sister before the racist persecution by the National Socialists from Germany via Switzerland and England to Canada (Ontario). He studied at the University of Toronto with a bachelor's degree in 1948 and a master's degree in 1949 and received his doctorate in 1951 from the University of Chicago with Irving Kaplansky ( Subrings of simple rings with minimal ideals ). He was then at the University of Michigan and from 1952 instructor and later associate professor at Northwestern University . 1961 to 1986 he was a professor at Cornell University , where he was head of the mathematics department from 1966 to 1969. From 1986 he was a professor at the University of California, Santa Barbara , where he headed the mathematics department in 1986/87 and retired in 1994. He lived in Schwerte for the last ten years.

From 1955 to 1957 he was at the Institute for Advanced Study in Princeton , 1961 to 1979 visiting professor at the University of California, Berkeley , 1963/64 visiting scholar at Queen Mary College, University of London, 1969/70 and 1982 at the University of California, Los Angeles , 1984/85 at the University of Dortmund, 1980 visiting professor at the University of Southern California and 1976 visiting professor at the ETH Zurich .

Rosenberg dealt with homological algebra , ring theory , Witt rings and quadratic forms. He applied the techniques of homological algebra newly developed in the 1940s and 1950s to Galois theory and to quadratic forms. The Hochschild-Kostant-Rosenberg theorem, which they proved in 1962, is named after him, Gerhard Hochschild and Bertram Kostant .

In 1975/76 he received a Humboldt Research Prize at the Ludwig Maximilians University in Munich with Bodo Pareigis , who had done his dissertation with him in the 1960s. Even Vera Pless was his graduate student.

From 1974 to 1983 he was a trustee of the American Mathematical Society . 1960 to 1965 he was editor of the Algebra section of the Proceedings of the American Mathematical Society and 1974 to 1976 of the American Mathematical Monthly . In the early 1970s, he directed the Mathematical Association of America's undergraduate program .

He had been married to Beatrice Gershenson from New York since 1952, with whom he had two sons and from whom he divorced in 1984. He also had an adopted son. Since 1985 he was married to Brunhilde Rosenberg (from Schwerte). He became a US citizen in 1959.

He should not be confused with the mathematician Alexander L. Rosenberg (1946–2012), a Soviet mathematician who was most recently a professor at Kansas State University.

Fonts (selection)

• The number of irreducible representations of simple rings with no minimal ideals, American Journal of Mathematics, Volume 75, 1954, pp. 523-530
• with Samuel Eilenberg . Dimension of rings and modules VIII, Tensor Products, Nagoya Math. J. Vol. 12, 1957, pp. 71-93
• with M. Auslander: Dimension of prime ideals in polynomial rings, Canadian Journal of Mathematics, Volume 10, 1958, pp. 287-293
• Blocks and centers of Group Algebras, Mathematische Zeitschrift, Volume 76, 1961, pp. 209-216
• with D. Zelinsky. Tensor products of semiprimary algebras, Duke Math. J., Vol. 23, 1957, pp. 555-560
• On the structure of the infinite linear group, Annals of Mathematics, Volume 68, 1958, pp. 278-294
• Finiteness of the injective hull, Mathematische Zeitschrift, Volume 70, 1959, pp. 372-380.
• with D. Harrison, SU Chase: Galois theory and galois cohomology of commutative rings, AMS Memoir 52, 1965, pp. 15-33;
• with R. Ware, M. Knebusch: Structure of Witt Rings and Quotients of Abelian Group Rings, American Journal of Mathematics, Volume 94, 1972, pp. 119-155
• with R. Ware, M. Knebusch: Signatures on Semilocal Rings, Journal of Algebra, Volume 26, 1973, pp. 208-250
• with TC Craven, R. Ware: The Map of the Witt Ring of a Domain into the Witt Ring of its Field of Fractions, Proc AMS 51, 1975, pp. 25-30.

literature

• Lance Small, Obituary in Notices AMS, May 2008, p. 613

Web links

• Obituary at Cornell University

Individual evidence

1. ↑ Birth and career dates for American Men and Women of Science , Thomson Gale 2004
2. ↑ Alex Rosenberg in the Mathematics Genealogy Project (English)
3. ↑ Hochschild-Kostant-Rosenberg theorem , nlab
4. ^ Hochschild, Kostant, Rosenberg, Differential forms on regular affine algebras, Transactions AMS, Volume 102, 1962, pp. 383-408