SOME ISOMORPHISMS IN DERIVED FUNCTORS AND THEIR APPLICATIONS

Let R be a commutative Noetherian ring, M be a finitely generated R-module and a be an ideal of R such that aM not equal M. We show among the other things that, if c is a nonnegative integer such that H-a(i) (M) = 0 for all i < c, then there is an isomorphism End(H-a(c) (M)) congruent to Ext(R)(c) (H-a(c) (M); M); and if c is a nonnegative integer such that H-a(i) (M) = 0 for all i not equal c, there are the following isomorphisms: (i) H-b(i) (H-a(c) (M)) congruent to H-b(i+c) (M) and (ii) Ext(R)(i) (R/b; H-a(c) (M)) congruent to Ext(R)(i+c) for all i is an element of N-0 and all ideals b of R with b superset of a. We also prove that if a and b are ideals of R with b superset of a and c : = grade(a, M), then there exists a natural homomorphism from End(H-a(c) (M)) to End(H-b(c) (M)), where grade(a, M) is the maximum length of M-sequences in a.