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Strong Artin-Rees Property in Rings of Dimension One and Two
Striuli, Janet
2007
Abstract
Let (R, m) be a local noetherian ring and let N \subseteq M
be two finitely generated R-modules such that the dim M/N \leq 1.
We give simple proof of the fact that there exists an integer h
such that I^n M \cap N = I^{n-h}(I^hM \cap N), for all n \geq h and for
all ideals I \subset R. We give upper bounds for such an integer h.
Moreover, we give two examples of rings of dimension two where
the property fails.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
39 (2007)
Subjects
Publisher
EUT Edizioni Università di Trieste
Source
Janet Striuli, "Strong Artin-Rees Property in Rings of Dimension One and Two”, in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 39 (2007), pp. 325–335.
Languages
en
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