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| Paper IPM / M / 8720 |
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| Abstract: | |
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Let R be a commutative Noetherian ring, \fraka be an ideal
of R and M be a finitely generated R-module, Melkersson and
Schenzel asked whether the set AssRExtiR(R/\frakaj,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(SuppRHi\fraka(M)) \leqslant s for all i with i < n, then
(i) the set ∪j > 0 SuppRExtiR(R/\frakaj, M))\geqslant s is finite for all i with i < n, and (ii) the set ∪j > 0 AssRExtiR(R/\frakaj, 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 ∈ T|dim(R/\frakp)\geqslant s}. Download TeX format |
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