On the Gorenstein property of the associated graded ring of a power of an ideal
- 23 Downloads
It has been proved by Herrmann, Ribbe and Schenzel that in a local ring the Gorensteiness of the associated graded ring of a power of an ideal implies the Gorensteiness of the associated graded ring of the ideal provided it is Cohen-Macaulay and the height of the ideal is at least two. We give a new proof to this theorem which covers also the height one case and so answer to a question of Herrmann, Ribbe and Schenzel whether their result holds for ideals of height one.
KeywordsExact Sequence Local Ring Residue Field Local Cohomology Local Duality
Unable to display preview. Download preview PDF.
- [GN]Goto S., andNishida K.: Filtrations and the Gorenstein property of the associated Rees algebras. PreprintGoogle Scholar
- [HRS]Herkmann, M. andRibbe, J. andSchenzel, P.: On the Gorenstein property of form rings. To appear in Math. Z.Google Scholar
- [Ma]Matsumura, N.: Commutative ring theory. Cambridge: Cambridge University Press 1988Google Scholar
- [O]Ooishi, A.: On the Gorenstein property of the Associated Graded King and the Kees algebra of an ideal. PreprintGoogle Scholar
- [R]Ribbe, J. : Zur Gerenstein-Eigenschaft yon Aufblasungsringen unter besonderer Berücksichtigung der Aufblasungsringe von Idealpotenzen. Dissertation, Universität zu Köln 1991Google Scholar