Maurice Auslander

Maurice Auslander (August 3, 1926 – November 18, 1994) was an American mathematician[1] who worked on commutative algebra, homological algebra and the representation theory of Artin algebras (e.g. finite-dimensional associative algebras over a field). He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras.

Born in Brooklyn, New York, Auslander received his bachelor's degree and his Ph.D. (1954) from Columbia University. He was a visiting scholar at the Institute for Advanced Study in 1956-57.[2] He was a professor at Brandeis University from 1957 until his death in Trondheim, Norway aged 68.[3] He was elected a Fellow of the American Academy of Arts and Sciences in 1971.[4]

Upon his death he was survived by his mother, his widow, a daughter, and a son.[3] His widow Bernice L. Auslander (November 21, 1931 - June 18, 2022) was a professor emerita of mathematics at University of Massachusetts at Boston.[5][6] As of 2022, his son Philip Auslander is a professor in the School of Literature, Media, and Communication at Georgia Tech,[7] and his daughter Leora Auslander is a professor of history at the University of Chicago.[8] Maurice Auslander's brother Louis Auslander was also a mathematician.[9]

Selected publications

Articles

• with David Buchsbaum: Homological dimension in Noetherian rings, Trans. Amer. Math. Soc., vol. 85, 1957, pp. 390–405 doi:10.2307/1992937
• with Oscar Goldman: The Brauer group of a commutative ring, Trans. Amer. Math. Soc., vol. 97, no. 3, 1960, pp. 367–409 doi:10.2307/1993378
• Modules over unramified regular local rings, Illinois J. Math., vol. 5, 1961, pp. 631–647
• with Idun Reiten: Representation theory of Artin algebras. III. Almost split sequences, Communications in Algebra, vol. 3, 1975, pp. 239–294 doi:10.1080/00927877508822046
• with Idun Reiten: On a generalized version of the Nakayama conjecture, Proc. Amer. Math. Soc., vol. 52, 1975, pp. 69–74 doi:10.1090/S0002-9939-1975-0389977-6

Books

• with Mark Bridger: Stable module theory, American Mathematical Society 1969
• with David Buchsbaum: Groups, rings, modules, Harper and Row 1974; Auslander, Maurice; Buchsbaum, David (2014). Dover reprint. Courier Corporation. ISBN 978-0-486-49082-3.[10]
• with Idun Reiten and Sverre O. Smalø: Representation theory of Artin algebras, Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, 1995 ISBN 0-521-41134-3[11]

References

Notes

1. O'Connor & Robertson, Maurice Auslander.
2. Institute for Advanced Study: A Community of Scholars Archived 2013-01-06 at the Wayback Machine
3. "Maurice Auslander, Mathematician, 68". New York Times. December 10, 1994. Retrieved 27 April 2011.
4. "Book of Members, 1780-2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 27 April 2011.
5. "Bernice Auslander". Chicago Jewish Funerals - Skokie Chapel; Chicago Tribune. June 18, 2022. Retrieved June 19, 2022.
6. Pierce, Kathleen (February 26, 2012). "Should it stay, or should it go? Downsizing during a move means making difficult decisions about what to keep". Boston Globe. Retrieved January 26, 2020.
7. "Philip Auslander". School of Literature, Media, and Communication, Georgia Tech.
8. "Leora Auslander Professor of European Social History". University of Chicago Department of History. Archived from the original on March 19, 2012. Retrieved March 11, 2012.
9. O'Connor & Robertson, Louis Auslander.
10. Stenger, Allen (26 November 2014). "Review of Groups, rings, modules by Maurice Auslander and David Buchsbaum". MAA Reviews, Mathematical Association of America.
11. Ringel, Claus Michael (1996). "Review of Representation theory of Artin algebras by Maurice Auslander, Idun Reiten, and Sverre Smalø" (PDF). Bull. Amer. Math. Soc. (N.S.). 33 (4): 509–517. doi:10.1090/S0273-0979-96-00683-0.

Sources

• Auslander, Maurice (1999), Reiten, Idun; Smalø, Sverre O.; Solberg, Øyvind (eds.), Selected works of Maurice Auslander. Part 1, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-0998-3, MR 1674397
• Auslander, Maurice (1999), Reiten, Idun; Smalø, Sverre O.; Solberg, Øyvind (eds.), Selected works of Maurice Auslander. Part 2, Providence, R.I.: American Mathematical Society, ISBN 978-0-8218-1000-2, MR 1674401
• Peskine, Christian; Reiten, Idun (1995), "Maurice Auslander (1926–1994)" (PDF), Notices of the American Mathematical Society, 42 (4): 450–453, ISSN 0002-9920, MR 1319276

External links

• Maurice Auslander Distinguished Lectures
• Maurice Auslander, Mathematician, 68, New York Times obituary
• O'Connor, John J.; Robertson, Edmund F., "Maurice Auslander", MacTutor History of Mathematics Archive, University of St Andrews
• Maurice Auslander at the Mathematics Genealogy Project