nLab David Buchsbaum

David Alvin Buchsbaum was an American algebraist, working mainly in commutative algebra and homological algebra. He was a student of Eilenberg with a Ph. D. thesis about Abelian categories.

• wikipedia: David Buchsbaum, Auslander-Buchsbaum theorem, Auslander-Buchsbaum formula
• mathematical obituary

Selected works

Work with a notion close to the notion of Quillen exact category

• D. A. Buchsbaum, A note on homology in categories, Ann. of Math. (2) 69 (1959) 66-74 MR140556

In a 1957 article with Maurice Auslander? they proved the Auslander-Buchsbaum formula on projective dimension of projective modules over commutative Noetherian local rings.

• Maurice Auslander?, David A. Buchsbaum, Homological dimension in local rings, Trans. Amer. Math. Soc. 85 (2): 390–405 (1957) doi MR0086822

In a 1959 article with Buchsbaum they proved the Auslander-Buchsbaum theorem? that every commutative Noetherian regular local ring is a unique factorization domain.

• Maurice Auslander?, David A. Buchsbaum, Unique factorization in regular local rings, Proc. Nat. Acad. Sci. 45 (5): 733-734 (1959) doi MR0103906

category: people