On the uniform behaviour of the Frobenius closures of ideals

K. Khashyarmanesh

Colloquium Mathematicae, Tome 107 (2007), p. 1-7 / Harvested from The Polish Digital Mathematics Library

Résumé

Let be a proper ideal of a commutative Noetherian ring R of prime characteristic p and let Q() be the smallest positive integer m such that ${(^{F})}^{[p^{m}]} =^{[p^{m}]}$ , where $^{F}$ is the Frobenius closure of . This paper is concerned with the question whether the set $Q (^{[p^{m}]}) : m \in ℕ ₀$ is bounded. We give an affirmative answer in the case that the ideal is generated by an u.s.d-sequence c₁,..., cₙ for R such that (i) the map $R / \sum_{j = 1}^{n} R c_{j} \to R / \sum_{j = 1}^{n} R c ²_{j}$ induced by multiplication by c₁...cₙ is an R-monomorphism; (ii) for all $\in a s s (c ₁^{j}, . . ., c ₙ^{j})$ , c₁/1,..., cₙ/1 is a $R_{}$ -filter regular sequence for $R_{}$ for j ∈ 1,2.

Publié le : 2007-01-01

Zbl 1115.13009

EUDML-ID : urn:eudml:doc:283979

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     author = {K. Khashyarmanesh},
     title = {On the uniform behaviour of the Frobenius closures of ideals},
     journal = {Colloquium Mathematicae},
     volume = {107},
     year = {2007},
     pages = {1-7},
     zbl = {1115.13009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-1}
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K. Khashyarmanesh. On the uniform behaviour of the Frobenius closures of ideals. Colloquium Mathematicae, Tome 107 (2007) pp. 1-7. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm109-1-1/