Abstract.
Let be an ideal of Noetherian ring R and let s be a non-negative integer. Let M be an R-module such that is finite R-module. If s is the first integer such that the local cohomology module is non -cofinite, then we show that is finite. In particular, the set of associated primes of is finite. Let be a local Noetherian ring and let M be a finite R-module. We study the last integer n such that the local cohomology module is not -cofinite and show that n just depends on the support of M.
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The research of the first author was supported in part by a grant from IPM (No. 83130114).
The second author was supported by a grant from University of Tehran (No. 6103023/1/01).
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Dibaei, M., Yassemi, S. Associated primes and cofiniteness of local cohomology modules. manuscripta math. 117, 199–205 (2005). https://doi.org/10.1007/s00229-005-0538-5
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DOI: https://doi.org/10.1007/s00229-005-0538-5