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.
[2] He was a professor at Brandeis University from 1957 until his death in Trondheim, Norway aged 68.
[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.