Abstract

Let G(I) be the associated graded ring of an ideal I in a Cohen-Macaulay local ring A. We give a sufficient condition for G(I) to be a Cohen-Macaulay ring. It is described in terms of the depths of A/In for finitely many n, the reduction numbers of IQ for certain prime ideals Q and the Artin-Nagata property of I in the sense of Ulrich (Contemp. Math. vol. 159, pp. 373-400). The main theorem unifies several results which are already known in this aspect of the theory. Although the statement of the main theorem is rather complicated, we restate the conditions under special situations, so that they are practical and simple.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1197-1213
Launched on MUSE
1996-12-01
Open Access
No
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