Expanded radical ideals and semiregular ideals
Expanded radical ideals and semiregular ideals
复制标题
扩展的激进理想和半正则理想
DOI：
--
复制
发表时间：
1973
期刊：
影响因子：
--
通讯作者：
M. Hochster
中科院分区：
文献类型：
--
作者：
M. Hochster
设R = K[xi，，wn]是一个多项式环，其中K是特征为零的域，通过将Xj映射到矩阵[y^]的子式上，将R嵌入到多项式环S-K [yij：1 ^ i ^ n -1，1 ^ j ^ n]中，矩阵[y^]的子式是通过删除第j列得到的.设I是R的齐次根理想。证明了如果IS是根，则I是半正则的，即R/I是Cohen-Macaulay。其他几个相关的结果将被建立，其中某些扩张的根理想保持根的事实要么暗示着，要么被暗示着，某些其他的理想是半正则的。这些结果中的每一个都与不变量理论有某种联系。
Let R = K[xi, , wn] be a polynomial ring, where K is a field of characteristic zero, and embed R in the polynomial ring S— K[yij: 1 ^ i ^ n — 1,1 ^ j ^ n] by mapping Xj to the minor of the matrix [y^] obtained by deleting the j t h column. Let I be a homogeneous radical ideal of R. It will be shown that if IS is radical, then / is semiregular, that is, R/I is Cohen-Macaulay. Several other related results will be established, in which the fact that certain expanded radical ideals remain radical either implies, or is implied by, the fact that certain other ideals are semiregular. Each one of these results has some connection with invariant theory.