Mathematical Biography of Melvin Hochster

摘要

Though commutative algebra had experienced two decades of strong growth during the 1950s and 1960s, it was still in its childhood. Notable successes-the proof of Auslander and Buchsbaum that regular local rings are unique factorization domains, the characterization of regularity as Noetherian local rings of finite global dimension by Auslander-Buchsbaum and Serre, and the characterization of rings of finite injective dimension by Bass-had paved the way for various homological conjectures, which largely came from the desire to understand modules of finite projective dimension or finite injective dimension.