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arXiv · 0711.4880

An upper bound on the reduction number of an ideal

Yayoi Kinoshita·Koji Nishida·Kensuke Sakata·Ryuta Shinya
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Abstract

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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Yayoi Kinoshita, Koji Nishida, Kensuke Sakata, Ryuta Shinya. 2007-11-30. An upper bound on the reduction number of an ideal. https://arxiv.org/abs/0711.4880

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