The index of reducibility of parameter ideals in low dimension

Details The index of reducibility of parameter ideals in low dimension The index of reducibility of parameter ideals in low dimension

2004-08-11

arxiv.org/abs/math/0408143v1

Mathematics

Commutative Algebra

12 pages. J. Algebra 278/2 (2004) 571-584 (to appear)

Scientific paper

Results are presented concerning the following question: If M is a finitely-generated module with finite local cohomologies over a Noetherian local ring (A, m), does there exist an integer n such that every parameter ideal for M contained in m^n has the same index of reducibility? We show that the answer is yes if M has dimension 1 or if M has dimension 2 and positive depth. This research is closely related to work of Goto-Suzuki and Goto-Sakurai; Goto-Sakurai have supplied an answer of yes in case M is Buchsbaum.

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