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      The noether map i

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      Author
      Neusel, M. D.
      Sezer, M.
      Date
      2009
      Source Title
      Forum Mathematicum
      Print ISSN
      0933-7741
      Electronic ISSN
      1435-5337
      Publisher
      Walter de Gruyter GmbH
      Volume
      21
      Issue
      4
      Pages
      567 - 578
      Language
      English
      Type
      Article
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      Abstract
      Let æ : G GL(n, F) be a faithful representation of a finite group G. In this paper we study the image of the associated Noether map J G G : F[V(G)]G → F [V]G. It turns out that the image of the Noether map characterizes the ring of invariants in the sense that its integral closure Im (JG G = F [V]G. This is true without any restrictions on the group, representation, or ground field. Moreover, we show that the extension Im(J G G) ⊆ F [V]G is a finite p-root extension if the characteristic of the ground field is p. Furthermore, we show that the Noether map is surjective, if V = Fn is a projective FG-module. We apply these results and obtain upper bounds on the degrees of a minimal generating set of FVG and the Cohen-Macaulay defect of FV G. We illustrate our results with several examples. © de Gruyter 2009.
      Permalink
      http://hdl.handle.net/11693/22700
      Published Version (Please cite this version)
      http://dx.doi.org/10.1515/FORUM.2009.028
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