Mori–Nagata theorem
In algebra, the Mori–Nagata theorem introduced by
Krull domains, where r is the number of minimal prime ideals
of A.
The theorem is a partial generalization of the Krull–Akizuki theorem, which concerns a one-dimensional noetherian domain. A consequence of the theorem is that if R is a Nagata ring, then every R-subalgebra of finite type is again a Nagata ring (Nishimura 1976).
The Mori–Nagata theorem follows from Matijevic's theorem. (McAdam 1990)
References
- McAdam, S. (1990), "Review: David Rees, Lectures on the asymptotic theory of ideals", Bull. Amer. Math. Soc. (N.S.), 22 (2): 315–317,
- Mori, Yoshiro (1953), "On the integral closure of an integral domain", Memoirs of the College of Science, University of Kyoto. Series A: Mathematics, 27: 249–256
- MR 0097388
- Nishimura, Jun-ichi (1976). "Note on integral closures of a noetherian integral domain". J. Math. Kyoto Univ. 16 (1): 117–122.
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