Minimal pure injective resolutions of flat modules
Minimal pure injective resolutions of flat modules
复制标题
平面模块的最小纯内射分辨率
DOI：
10.1016/0021-8693(87)90200-6
复制
发表时间：
1987
影响因子：
0.9
通讯作者：
E. Enochs
中科院分区：
文献类型：
--
作者：
E. Enochs
每个模块都有一个最小的纯单射分辨率。对于诺特环上的平坦模，以这种分辨率出现的纯单射模的结构现在是已知的，并且可以用于给出有关平坦模的最小纯单射分辨率的信息。这些信息反过来可以用来提供有关平面模块投影尺寸的新结果证明，同时使这些结果更加清晰。环定理的变化给出了也许令人惊讶的结果，即在某些固定地面域上的仿射代数簇的坐标环的纯内射维数对于给定维度的所有簇来说是相同的。
Every module has a minimal pure injective resolution. For a flat modul over a noetherian ring, the structure of the pure injective modules appearing in such a resolution is now known and can be used to give information about minimal pure injective resolutions of flat modules. This information can in turn be used to give new proofs of results about the projective dimension of flat modules and at the same time sharpen these results. A change of ring theorem gives the perhaps surprising result that the pure injective dimensions of the coordinate rings of affine algebraic varieties over some fixed ground field are the same for all varieties of a given dimensionn.