Geodesic
Symbolic Powers of Regular Primes
Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1331-1337

Voir la notice de l'article provenant de la source Cambridge University Press

In a recent paper [6], P. Seibt has obtained the following result: Let k be a field of characteristic 0, k[T 1, ... , Tr ] the polynomial ring in r indeterminates over k, and let P be a prime ideal of k[T 1, ... , Tr ]. Then a polynomial F belongs to the n-th symbolic power P (n) of P if and only if all higher derivatives of F from the 0-th up to the (n – l)-st order belong to P.In this work we shall naturally generalize this result so as to be valid for primes of the polynomial ring over a perfect field k. Actually, we shall get a generalization as a corollary to a theorem which asserts: For regular primes P in a k-algebra R of finite type, a certain differential filtration of R associated with P coincides with the symbolic power filtration (P (n))n≧0. 
Ishibashi, Yasunori. Symbolic Powers of Regular Primes. Canadian journal of mathematics, Tome 33 (1981) no. 6, pp. 1331-1337. doi: 10.4153/CJM-1981-102-2
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