Let R be a commutative Noetherian ring, a be an ideal of R and M be a finitely generated R- module. Melkersson and Schenzel asked whether the set Ass(R)Ext(R)(i) R( R/ a (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 >= 0 and n >= 0 such that dim(Supp(R)H(a)(i) a( M)) <= s for all i with i < n, then (i) the set (U-j>0 Supp(R)Ext(R)(i) (R/a(j), M))(>= s) is finite for all i with i <= n, and (ii) the set (U-j>0 Ass(R)Ext(R)(i) (R/a(j), M))(>= s) is finite for all i with i <= n, where for a subset T of Spec(R), we set (T)(>= s) := {p epsilon T | dim(R/p) >= s}. Also, among other things, we show that if n >= 0, R is semi- local and Supp(R)H(a)(i)( ) is finite for all i with i < n, then U-j>0 Ass(R)Ext(R)(i) (R/a(j), M) is finite for all i with i <= n.
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