%0 Journal Article
%T A Necessary and Sufficient Condition for Determining a Hilbert Basis of P_n(Γ)<br>判定P_n(Γ)的Hilbert基的一个充要
%A Cen Yanming
%A <br>贵州民族学院数学系
%A />
%A />华中科学技术大学
%J 数学物理学报(A辑)
%D 2004
%I 
%X Let Γ be a compact Lie group acting on R^n and P_n(Γ) the ring of Γ invariant polynomial germs under Γ. Hilbert-Weyl theorem shows that there is a Hilbert basis consisting of Γ invariant homogeneous polynomial germs for P_n(Γ). However, it is not clear, how to choose a Hilbert basis from Γ invariant homogeneous polynomial germs and how to determine that a finite set of Γ invariant homogeneous polynomial germs is a Hilbert basis of P_n(Γ).  In this paper, by means of some fundamental properties of Noether's ring and invariant integration as well as the relevant theorems in the theory of singularities, a necessary and sufficient condition is  proved for determining a Hilber basis of P_n(Γ). This will provide a new way to determine of a Hilbert basis for some P_n(Γ).
%K Compact Lie group
%K Ring of invariant polynomial germs
%K Hilbert basis<br>紧李群
%K 不变多项式芽环
%K Hilbert基
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=37F46C35E03B4B86&jid=4DB553CDB5F521D8C921082E5C95EC80&aid=7C8B3F657A52FCDC&yid=D0E58B75BFD8E51C&vid=B91E8C6D6FE990DB&iid=E158A972A605785F&sid=8F2250DA83AF77B8&eid=FE6B7E9BDCCDBAA6&journal_id=1003-3998&journal_name=数学物理学报(A辑)&referenced_num=0&reference_num=5