Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4116
 Title: Strong Artin-Rees Property in Rings of Dimension One and Two Authors: Striuli, Janet Keywords: Artin-Rees Lemma Issue Date: 2007 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. Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics39 (2007) Abstract: Let (R, m) be a local noetherian ring and let N \subseteq Mbe 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 hsuch that I^n M \cap N = I^{n-h}(I^hM \cap N), for all n \geq h and forall ideals I \subset R. We give upper bounds for such an integer h.Moreover, we give two examples of rings of dimension two wherethe property fails. Type: Article URI: http://hdl.handle.net/10077/4116 ISSN: 0049-4704 Appears in Collections: Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.39 (2007)

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