The theorem was first proved by Maurice Auslander and David Buchsbaum (1959). They showed that regular local rings of dimension 3 are unique factorization domains, and Masayoshi Nagata (1958) had previously shown that this implies that all regular local rings are unique factorization domains.
- Auslander, Maurice; Buchsbaum, D. A. (1959), "Unique factorization in regular local rings", Proceedings of the National Academy of Sciences of the United States of America 45: 733–734, ISSN 0027-8424, JSTOR 90213, MR 0103906
- Nagata, Masayoshi (1958), "A general theory of algebraic geometry over Dedekind domains. II. Separably generated extensions and regular local rings", American Journal of Mathematics 80: 382–420, ISSN 0002-9327, JSTOR 2372791, MR 0094344