Auslander–Buchsbaum theorem
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. References

Commutative algebra
Theorems in ring theory