On form ideals and Artin-Rees condition |
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Authors: | Luca Chiantini |
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Institution: | (1) Istituto Matematico del Politecnico, Corso Duca degli Abruzzi 24, 10129 Torino, Italia |
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Abstract: | We look for conditions which make two ideals and in a noetherian ring A have the same form ideal in an associated graded ring GA(α). More precisely, when and and fi?f'iεα m m?0, ? i , we give a necessary and sufficient condition to have , involving the first syzygies modules both of (f1,...,fn) and (f'1,...,f'n); our proof is based on the Artin-Rees lemma. Finally we show that, when the sequence f1,...,fn is regular and for an integer q, then f1?f'i ? αq+1 ? i implies . |
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