Auslander–Buchsbaum theorem: Difference between revisions

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In commutative algebra, the Auslander–Buchsbaum theorem states that regular local rings are unique factorization domains.

The theorem was first proved by Maurice Auslander and 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.

References

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, MR0103906
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, MR0094344

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	In commutative algebra, the '''Auslander–Buchsbaum theorem''' states that [[regular local ring]]s are [[unique factorization domain]]s.		In [[commutative algebra]], the '''Auslander–Buchsbaum theorem''' states that [[regular local ring]]s are [[unique factorization domain]]s.

	The theorem was first proved by {{harvs\|txt\|first=Maurice\|last=Auslander\|authorlink=Maurice Auslander\|last2=Buchsbaum\|author2-link=David Buchsbaum\|year=1959}}. They showed that regular local rings of dimension 3 are unique factorization domains, and {{harvs\|txt\|first1=Masayoshi \| author1-link=Masayoshi Nagata \|last=Nagata\|year=1958}} had previously shown that this implies that all regular local rings are unique factorization domains.		The theorem was first proved by {{harvs\|txt\|first=Maurice\|last=Auslander\|authorlink=Maurice Auslander\|last2=Buchsbaum\|author2-link=David Buchsbaum\|year=1959}}. They showed that regular local rings of dimension 3 are unique factorization domains, and {{harvs\|txt\|first1=Masayoshi \| author1-link=Masayoshi Nagata \|last=Nagata\|year=1958}} had previously shown that this implies that all regular local rings are unique factorization domains.