Growth in the minimal injective resolution of a local ring
Growth in the minimal injective resolution of a local ring
复制标题
局部环最小注入分辨率的增长
DOI：
10.1112/jlms/jdp058
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Oana Veliche
中科院分区：
文献类型：
--
作者：
Lars Christensen;J. Striuli;Oana Veliche
设R是具有剩余域k的交换Noether局部环，且R不是Gorenstein环.在R的最小内射分解中，剩余域的内射包络E在从R的深度开始的每一次上都表现为被加数。E在i次的拷贝数等于上同调模ExtiR（k，R）的k向量空间维数。这些维度，被称为巴斯数，形成了R的不变量的无限序列，对此知之甚少。我们证明了它是非递减的，并且指数增长，如果R是Golod，一个非平凡的纤维积，或Teter，或者如果它有根立方零。
Let R be a commutative noetherian local ring with residue field k and assume that it is not Gorenstein. In the minimal injective resolution of R, the injective envelope E of the residue field appears as a summand in every degree starting from the depth of R. The number of copies of E in degree i equals the k‐vector space dimension of the cohomology module ExtiR(k, R). These dimensions, known as Bass numbers, form an infinite sequence of invariants of R about which little is known. We prove that it is non‐decreasing and grows exponentially if R is Golod, a non‐trivial fiber product, or Teter, or if it has radical cube zero.