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...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）.展开更多
文摘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）.
