Generalizations of a lemma of Freudenburg |
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| Authors: | Arno van den Essen Andrzej Nowicki Andrzej Tyc |
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| Institution: | a Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands
b Faculty of Mathematics and Informatics, N. Copernicus University, 87-100 Toruń, Poland |
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| Abstract: | Let k be an algebraically closed field of characteristic zero and ℘ a prime ideal in kX]?kX1,…,Xn]. Let g∈kX] and d?1. If for all 1?|α|?d the derivatives ∂αg belong to ℘, then there exists c∈k such that g−c∈℘(d+1), the d+1th symbolic power of ℘. In particular, if ℘ is a complete intersection it follows that g−c∈℘d+1. |
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| Keywords: | 13C99 13C40 13P10 |
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