Abstract
Let I be an ideal of a local ring (R, 𝔪). Using local cohomology, we present new criteria (see 1.4, respectively 1.5) for the conditions ara (I) ≤ 1 respectively ara (I) ≤ 2, where ara (I) stands for the number of generators of I up to radical. Though this works equally well for the local and for the graded case, we show some subtle differences between the local and the graded situation in Section 2. Finally, in Section 3, we show that the Matlis dual of certain local cohomology modules, though not finite, is well behaved in some sense.
Mathematics Subject Classification:
Notes
Communicated by W. Bruns.