Asymptotic stability of depths of localizations of modules
| Autor: | Kimura, Kaito |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let R be a commutative noetherian ring, I an ideal of R, and M a finitely generated R-module. The asymptotic behavior of the quotient modules M/I^n M of M is an actively studied subject in commutative algebra. The main result of this paper asserts that the depth of the localization of M/I^n M at any prime ideal of R is stable for large integers n that do not depend on the prime ideal, if the module M or M/I^n M is Cohen-Macaulay for some n>0, or the ring R is one of the following: a homomorphic image of a Cohen-Macaulay ring, a semi-local ring, an excellent ring, a quasi-excellent and catenary ring, and an acceptable ring. Comment: 8 pages |
| Databáze: | arXiv |
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