Let (R, m,k) be a Noetherian local ring of prime characteristic p and d its Krull dimension. It is known that for an m-primary ideal I of R and a finitely generated R-module N the limit lim IR(N/I[n]N)/pdn esists where I[n] denotes the ideal of R generated by xpn, xI, and LR(M) the length of an R-module M.
展开▼
机译：令（R，m，k）为主要特征p的Noetherian局部环，d为Krull维度。已知对于R的m-基数理想I和有限生成的R-模N，极限lim IR（N / I [n] N）/ pdn存在，其中I [n]表示由xpn生成的R的理想，xI和LR（M）表示R模块M的长度。
展开▼
