| Title:
|
On the non-vanishing of local cohomology modules (English) |
| Author:
|
Yassemi, Siamak |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
1997 |
| Pages:
|
585-592 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that for any Artinian modules $M$, $\dim M^{\vee }$ is the greatest integer $i$ such that ${\mbox{H}}^i_{\mathfrak m}(M^{\vee })\ne 0$. (English) |
| MSC:
|
13D45 |
| MSC:
|
13E10 |
| idZBL:
|
Zbl 0901.13014 |
| idMR:
|
MR1479306 |
| . |
| Date available:
|
2009-09-24T10:08:37Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127380 |
| . |
| Reference:
|
[1] A. Grothendick (notes by R. Hartshorne): Local Cohomology.Lecture Notes in Math. 41, Springer Verlag, 1967. MR 0224620 |
| Reference:
|
[2] H.-B. Foxby: A homological theory of complexes of modules.Preprint Series No. 19a & 19b, Dept. of Mathematics, Univ. Copenhagen, 1981. |
| Reference:
|
[3] I.G. Macdonald: Secondary representation of modules over a commutative ring.Symp. Math. XI (1973) 23–43. Zbl 0271.13001, MR 0342506 |
| Reference:
|
[4] I. G. Macdonald and R. Y. Sharp: An elementary proof of the non-vanishing of certain local cohomology modules.Quart. J. Math. (Oxford)(2) 23 (1970), 197–204. MR 0299598, 10.1093/qmath/23.2.197 |
| Reference:
|
[5] R.Y. Sharp: Local cohomology theory in commutative algebra.Quart. J. Math. (Oxford) (2) 21 (1970), 425–434. Zbl 0204.06003, MR 0276217, 10.1093/qmath/21.4.425 |
| Reference:
|
[6] S. Yassemi: Coassociated primes.Comm. Algebra 23 (1995), 1473–1498. Zbl 0832.13004, MR 1317409, 10.1080/00927879508825288 |
| Reference:
|
[7] S. Yassemi: Magnitude of modules.Comm. Algebra 23 (1995), 3993–4008. Zbl 0836.13005, MR 1351115, 10.1080/00927879508825445 |
| . |
