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On the finiteness properties of Matlis duals of local cohomology modules
| Content Provider | Semantic Scholar |
|---|---|
| Author | Khashyarmanesh, Kazem |
| Copyright Year | 2008 |
| Abstract | Let R be a complete semi-local ring with respect to the topology defined by its Jacobson radical, a an ideal of R, and M a finitely generated R-module. Let DR(−) := HomR(−, E), where E is the injective hull of the direct sum of all simple R-modules. If n is a positive integer such that ExtjR(R/a, DR(H t a(M))) is finitely generated for all t > n and all j 0, then we show that HomR(R/a, DR(H a (M))) is also finitely generated. Specially, the set of prime ideals in CoassR(H a (M)) which contains a is finite. Next, assume that (R, m) is a complete local ring. We study the finiteness properties of DR(H a (R)) where r is the least integer i such that H i a(R) is not Artinian. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://www.ias.ac.in/article/fulltext/pmsc/118/02/0197-0206 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
