Amir Mafi

Let R be a commutative Noetherian ring, a an ideal of R, and M, N two nitely generated R-modules. Let t be a non-negative integer. It is shown that for any nitely generated R-module L with Supp(L)  Supp(M), the following statements hold: (i) Supp(Extt R(L;N))  [t i=0 Supp(Exti R(M;N)); (ii) Ass(Extt R(L;N))  Ass(Extt R(M;N)) [ ([t􀀀1 i=0 Supp(Exti R(M;N))). As an immediate consequence, we deduce that if Supp(Hi a(N)) or Supp(Hi a (M;N)) is nite for all i < t, then the set [n2N Ass(Extt R(M=anM;N)) is - nite. In particular, if grade(a;N)  t then the set [n2N Ass(Extt R(M=anM;N)) is nite.