Gourmet's Guide to Gorensteinness
Gourmet's Guide to Gorensteinness
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DOI：
10.1006/aima.1999.1897
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发表时间：
2000-05
影响因子：
1.7
通讯作者：
Peter Jørgensen;James J. Zhang
中科院分区：
文献类型：
--
作者：
Peter Jørgensen;James J. Zhang
如果我们很聪明的话，我们也许能够解决下面的问题：设A是由生成元和关系给出的Noether N阶化连通k代数现在通过观察关系来确定A是否是AS Gorenstein然而，必须承认，所述问题似乎相当困难，因此，一个更温和的目标是下面找到一些标准，通过这些标准可以确定某些自然出现的代数是否是AS Gorenstein这就是我们在这本手册中要做的。我们证明了交换代数中几个著名定理的推广，特别是Watanabe定理thm和Stanley定理thm。主要结果如下：注意，在这本手稿中，代数表示N阶连通k代数定理Watanabe定理设A是具有对偶A的Noether AS正则代数，设G是一个群，令
If we were very clever we might be able to solve the following prob lem Let A be a noetherian N graded connected k algebra given by generators and relations Now determine by looking at the relations if A is AS Gorenstein It must however be admitted that the problem as stated seems rather hard A more modest goal is hence the following Find some criteria by which it can be decided whether some naturally occuring algebras are AS Gorenstein That is what we shall do in this manu script We prove generalizations of several well known theorems from com mutative algebra notably Watanabe s theorem thm and Stanley s theorem thm The main results are the follow ing note that throughout this manuscript algebra means N graded connected k algebra Theorem Watanabe Let A be a noetherian AS regular algebra with dual A let G be a group and let