Auslander–Buchsbaum theorem should not be confused with Auslander–Buchsbaum formula.
In commutative algebra, the Auslander–Buchsbaum theorem states that regular local rings are unique factorization domains.
The theorem was first proved by . They showed that regular local rings of dimension 3 are unique factorization domains, and had previously shown that this implies that all regular local rings are unique factorization domains.