Maurice Auslander (August 3, 1926 – November 18, 1994) was an American mathematician who worked on

commutative algebra Commutative algebra, first known as ideal theory, is the branch of algebra that studies commutative rings, their ideal (ring theory), ideals, and module (mathematics), modules over such rings. Both algebraic geometry and algebraic number theo ...

homological algebra Homological algebra is the branch of mathematics that studies homology (mathematics), homology in a general algebraic setting. It is a relatively young discipline, whose origins can be traced to investigations in combinatorial topology (a precurs ...

and the

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

of Artin algebras (e.g. finite-dimensional associative algebras over a field). He proved the Auslander–Buchsbaum theorem that regular local rings are

factorial In mathematics, the factorial of a non-negative denoted is the Product (mathematics), product of all positive integers less than or equal The factorial also equals the product of n with the next smaller factorial: \begin n! &= n \times ...

, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras. Born in

Brooklyn Brooklyn is a Boroughs of New York City, borough of New York City located at the westernmost end of Long Island in the New York (state), State of New York. Formerly an independent city, the borough is coextensive with Kings County, one of twelv ...

, New York, Auslander received his bachelor's degree and his Ph.D. (1954) from

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

. He was a visiting scholar at the

Institute for Advanced Study The Institute for Advanced Study (IAS) is an independent center for theoretical research and intellectual inquiry located in Princeton, New Jersey. It has served as the academic home of internationally preeminent scholars, including Albert Ein ...

in 1956-57. He was a professor at

Brandeis University Brandeis University () is a Private university, private research university in Waltham, Massachusetts, United States. It is located within the Greater Boston area. Founded in 1948 as a nonsectarian, non-sectarian, coeducational university, Bra ...

from 1957 until his death in

Trondheim Trondheim ( , , ; ), historically Kaupangen, Nidaros, and Trondhjem (), is a city and municipality in Trøndelag county, Norway. As of 2022, it had a population of 212,660. Trondheim is the third most populous municipality in Norway, and is ...

Norway Norway, officially the Kingdom of Norway, is a Nordic countries, Nordic country located on the Scandinavian Peninsula in Northern Europe. The remote Arctic island of Jan Mayen and the archipelago of Svalbard also form part of the Kingdom of ...

aged 68. He was elected a Fellow of the

American Academy of Arts and Sciences The American Academy of Arts and Sciences (The Academy) is one of the oldest learned societies in the United States. It was founded in 1780 during the American Revolution by John Adams, John Hancock, James Bowdoin, Andrew Oliver, and other ...

in 1971. Upon his death he was survived by his mother, his widow, a daughter, and a son. His widow Bernice L. Auslander (November 21, 1931 - June 18, 2022) was a professor emerita of mathematics at University of Massachusetts at Boston. As of 2022, his son Philip Auslander is a professor in the School of Literature, Media, and Communication at Georgia Tech, and his daughter Leora Auslander is a professor of history at the

University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...

. Maurice Auslander's brother Louis Auslander was also a mathematician.

Selected publications

Articles

*with

David Buchsbaum David Alvin Buchsbaum (November 6, 1929 – January 8, 2021) was a mathematician at Brandeis University who worked on commutative algebra, homological algebra, and representation theory. He proved the Auslander–Buchsbaum formula and the Ausland ...

: ''Homological dimension in Noetherian rings'', Trans. Amer. Math. Soc., vol. 85, 1957, pp. 390–405 *with Oscar Goldman: ''The Brauer group of a commutative ring'', Trans. Amer. Math. Soc., vol. 97, no. 3, 1960, pp. 367–409
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 *with Idun Reiten: ''On a generalized version of the Nakayama conjecture'', Proc. Amer. Math. Soc., vol. 52, 1975, pp. 69–74

Books

*with Mark Bridger
''Stable module theory''
American Mathematical Society 1969 *with David Buchsbaum: ''Groups, rings, modules'', Harper and Row 1974; *with Idun Reiten and Sverre O. Smalø: ''Representation theory of Artin algebras'', Cambridge Studies in Advanced Mathematics, 36, Cambridge University Press, 1995

References

;Notes ;Sources * * *

External links

Maurice Auslander Distinguished Lectures
New York Times obituary * * 1926 births 1994 deaths 20th-century American mathematicians American algebraists Brandeis University faculty Columbia University alumni Fellows of the American Academy of Arts and Sciences Institute for Advanced Study visiting scholars Mathematicians from Brooklyn {{US-mathematician-stub