An upper bound on the reduction number of an ideal

Details An upper bound on the reduction number of an ideal An upper bound on the reduction number of an ideal

2007-11-30

arxiv.org/abs/0711.4880v1

Mathematics

Commutative Algebra

9 pages

Scientific paper

Let A be a commutative ring and I an ideal of A with a reduction Q. In this
paper we give an upper bound on the reduction number of I with respect to Q,
when a suitable family of ideals in A is given. As a corollary it follows that
if some ideal J containing I satisfies J^2 = QJ, then I^{v + 2} = QI^{v + 1},
where v denotes the number of generators of J / I as an A-module.

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