Notes on the behavior of the Ratliff-Rush filtration

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We establish new classes of Ratliff-Rush closed ideals and some pathological behavior of the Ratliff-Rush closure. In particular, Ratliff-Rush closure does not behave well under passage modulo superficial elements, taking powers of ideals, associated primes, leading term ideals, and the minimal number of generators. In contrast, the reduction number of the Ratliff-Rush filtration behaves better: it preserves some information on the reduction number of the ideal.

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Commutative Algebra, 13A30, 13B22, 13P10

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http://salesiana.dossiersoluciones.com/handle/123456789/65048

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0209308
 http://arxiv.org/abs/math/0209308

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arXiv