Ideals defined by matrices and a certain complex associated with them
Ideals defined by matrices and a certain complex associated with them
复制标题
由矩阵和与其相关的特定复形定义的理想
DOI：
--
复制
发表时间：
1962
期刊：
影响因子：
--
通讯作者：
D. Northcott
中科院分区：
文献类型：
--
作者：
J. Eagon;D. Northcott
对于元素属于具有单位元的交换环的每个矩阵，定义了一个自由复形。该复形是标准Koszul复形的推广，它对应于只有一行的矩阵的情况。它适用于由矩阵的极大子行列式定义的某些理想。我们发现，当理想的级数达到某一最大值(取决于矩阵的维度)时，这种理想的射影维度是有限的，并且在这种情况下，复形提供了正确长度的自由分辨。对于半正则(=M acaulayCohen)环，这得到了关于非混合理想的一个定理。在任意Noether环的情况下，证明了一个关于秩的一般定理。
For each matrix, whose elements belong to a commutative ring with an identity element, there is defined a free complex. This complex is a generalization of the standard Koszul complex, which corresponds to the case of a matrix with only a single row. The applications are to certain ideals defined by the maximal subdeterminants of a matrix. It is found that such an ideal has finite projective dimension whenever its grade reaches a certain greatest value (depending on the dimensions of the matrix) and that, in these circum stances, the complex provides a free resolution of the correct length. For semi-regular ( = M acaulayCohen) rings this leads to a theorem on unmixed ideals. In the case of arbitrary Noetherian rings, a general theorem on rank is proved.