local cohomology;
associated prime ideals;
cofiniteness;
weakly Laskerian modules;
spectral sequences;
D O I:
10.1090/S0002-9939-04-07728-7
中图分类号:
O29 [应用数学];
学科分类号:
070104 ;
摘要:
Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. Let t be a natural integer. It is shown that there is a finite subset X of Spec R, such that Ass(R)(H-a(t)(M)) is contained in X union with the union of the sets Ass(R)(Ext(R)(j)(R/a, H-a(i)(M))), where 0 less than or equal to i < t and 0 <= j <= t(2) + 1. As an immediate consequence, we deduce that the first non-a-cofinite local cohomology module of M with respect to a has only finitely many associated prime ideals.