Depth Formulas, Restricted Tor-Dimension under Base Change
Depth Formulas, Restricted Tor-Dimension under Base Change
复制标题
DOI：
10.1216/rmjm/1181069847
复制
发表时间：
2004-09
影响因子：
0.8
通讯作者：
Tirdad Sharif;S. Yassemi
中科院分区：
文献类型：
--
作者：
Tirdad Sharif;S. Yassemi
。设R是交换Noether环，M和N是R-模。证明了如果M在维上有−nitefifl，则sup{i|Tor Ri(M，N)(Cid：1)=0}=sup{Depth Rp−Depth Rp Mp−Depth Rp Np|p∈Supp M∩Supp N}.设R是完备局部环，M是fiNite-生成R-模，N是fi-Nitefl的维R-模。证明了sup{i|Ext Ir(N，M)(Cid：1)=0}=Depth R−Depth N offinite维}。此外，还给出了一些关于变基情况下的TD-R-M的结果。
. Let R be a commutative Noetherian ring, and let M and N be R -modules. It is shown that sup { i | Tor Ri ( M,N ) (cid:1) =0 } = sup { depth R p − depth R p M p − depth R p N p | p ∈ Supp M ∩ Supp N } provided that M has finite flat dimension. Assume that R is a complete local ring, M a finitely generated R -module, and N an R -module of finite flat dimension. It is then proved that sup { i | Ext iR ( N,M ) (cid:1) = 0 } = depth R − depth N. of finite dimension } . In addition, some results concerning Td R M under base change are given.