Nagata criterion for Serre’s \((R_n)\) and \((S_n)\)-conditions. (English) Zbl 0990.14001
Let \(A\) be a commutative, noetherian ring. Nagata’s criterion gives an axiomatic procedure for proving that some geometric loci of Spec\((A)\) are open. The author shows directly that Nagata’s criterion applies to the loci of primes satisfying Serre’s \((R_n)\) or \((S_n)\) regularity conditions (for all \(n\geq 0\)), and hence these loci are open in Spec(\(A\)).
Reviewer: L.Chiantini (Siena)
MSC:
14A05 | Relevant commutative algebra |
13A15 | Ideals and multiplicative ideal theory in commutative rings |