Property of Almost Cohen-Macaulay over Extension Modules

• 来源期刊: 代数集刊（英文版）
• 关键词: almost Cohen-Macaulay module Ext functor finiteness dimension
• 年，卷（期）: 2017,（3）
• 页码范围: 509-518
• 页数: 10页
• 语种: 英文
• DOI: 10.1142/S1005386717000335

摘要

Let (R,m) be a Cohen-Macaulay local ring of dimension d,C a canonical R-module and M an almost Cohen-Macaulay R-module of dimension n and of depth t.We prove that dim Extd-nR(M,C) =n and if n ≤ 3 then Extd-nR(M,C) is an almost Cohen-Macaulay R-module.In particular,if n =d ≤ 3 then HomR(M,C) is an almost Cohen-Macaulay R-module.In addition,with some conditions,we show that Ext1R(M,C) is also almost Cohen-Macaulay.Finally,we study the vanishing ExtiR (Extd-nR(M,C),C) and ExtiR (Extd-tR (M,C),C).