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Paper IPM / M / 7713  


Abstract:  
Let \fraka be an ideal of Noetherian ring R and
let s be a nonnegative integer. Let M be an Rmodule such
that Ext^{s}_{R}(R/ \fraka,M) is finite Rmodule. If s is the
first integer such that the local cohomology module
H^{s}_{\frak}a(M) is non \frakacofinite, then we show that
Hom_{R}(R/ \fraka, H^{s}_{a}(M)) is finite. In particular, the set
of associated primes
of H^{s}_{\frak}a(M) is finite. (R, \frakm) be a local Noetherian ring and let M be a
finite Rmodule. We study the last integer n such that the
local cohomology module H^{n}_{\frak}a(M) is not
\frakmcofinite and show that n just depends on the support
of M.
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