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Paper IPM / M / 8720  


Abstract:  
Let R be a commutative Noetherian ring, \fraka be an ideal
of R and M be a finitely generated Rmodule, Melkersson and
Schenzel asked whether the set Ass_{R}Ext^{i}_{R}(R/\fraka^{j},M) becomes stable for a fixed integer i and sufficiently large
j. This paper is concerned with this question. In fact, we prove
that if s\geqslant 0 and n\geqslant 0 such that
dim(Supp_{R}H^{i}_{\frak}a(M)) \leqslant s for all i with i < n, then
(i) the set ∪_{j > 0} Supp_{R}Ext^{i}_{R}(R/\fraka^{j}, M))_{\geqslant s} is finite for all i with i < n, and (ii) the set ∪_{j > 0} Ass_{R}Ext^{i}_{R}(R/\fraka^{j}, M))_{\geqslant s} is finite for all i with i \leqslant n, where for a subset T of Spec(R), we set (T)_{\geqslant s}: {\frakp ∈ Tdim(R/\frakp)\geqslant s}. Download TeX format 

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