The reductions of an ideal I give a natural pathway to the properties of I, with the advantage of having fewer generators. In this paper we primarily focus on a conjecture about the reduction exponent of links of a broad class of primary ideals. The existence of an algebra structure on the Koszul and Eagon-Northcott resolutions is the main tool for detailing the known cases of the conjecture. In the last section we relate the conjecture to a formula involving the length of the first Koszul homology modules of these ideals.
|Number of pages||15|
|Journal||Journal of Pure and Applied Algebra|
|State||Published - Sep 11 1997|
Bibliographical noteFunding Information:
The authors wish to acknowledge Wolmer V. Vasconcelos, for useful discussions they had during the writing of this paper, and Bemd Ulrich, for helpful suggestions which improved the exposition of Section 3. Both authors gratefully acknowledge partial support from the Consiglio Nazionale delle Ricerche, Italy, under CNR grant 203.01.63.
ASJC Scopus subject areas
- Algebra and Number Theory