Notes on the behavior of the Ratliff-Rush filtration
By M. Rossi, Irena Swanson. 2002
49 citations recorded by the source corpus.
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. Let I be an ideal in a Noetherian ring R. From the maximal condition it follows that there exist ideals e I in R maximal with respect to the condition e I n = I n for all large n.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/1aea3bccb985f842d2050a46d5de7d5706f7cf74
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In Algebra and Number Theory
In Computational Theory and Mathematics
Citations in the corpus
- Hilbert Functions of Filtered Modules (2007, methodology): “Examples are given by Rossi and Swanson in [81].”