Property of Almost Cohen-Macaulay over Extension Modules  

作　　者：Samaneh Tabejamaat Amir Mafi Khadijeh Ahmadi Amoli Samaneh Tabejamaat Amir Mafi Khadijeh Ahmadi Amoli(Department of Mathematics, Payame Noor University P.O.Box： 19395-3697, Tehran, Iran Department of Mathematics, University of Kurdistan P.O. Box： 416, Sanandaj, Iran Department of Mathematics, Payame Noor University P.O.Box： 19395-3697, Tehraa, Iran)

机构地区：[1]Department of Mathematics, Payame Noor University P.O.Box: 19395-3697, Tehran, Iran [2]Department of Mathematics, University of Kurdistan P.O. Box: 416, Sanandaj, Iran [3]Department of Mathematics, Payame Noor University P.O.Box: 19395-3697, Tehraa, Iran

出　　处：《Algebra Colloquium》2017年第3期509-518,共10页代数集刊（英文版）

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-n R（M,C） = n and if n ≤ 3 then Extd-n（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 Ext2R （Extd-n （M, C）, C） and Ext2R （Extd-n（M, C）, C）.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-n R（M,C） = n and if n ≤ 3 then Extd-n（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 Ext2R （Extd-n （M, C）, C） and Ext2R （Extd-n（M, C）, C）.

关 键 词：almost Cohen-Macaulay module Ext functor finiteness dimension 

分 类 号：O241.1[理学—计算数学] TP273.3[理学—数学]