Artinian cofinite modules over complete Noetherian local rings

Let (R, m) be a complete Noetherian local ring, I an ideal of R and M a nonzero Artinian R-module. In this paper it is shown that if p is a prime ideal of R such that dim R/p = 1 and (0:M p) is not finitely generated and for each i a (c) 3/4 2 the R-module Ext (R) (i) (M,R/p) is of finite length, then the R-module Ext (R) (1) (M, R/p) is not of finite length. Using this result, it is shown that for all finitely generated R-modules N with Supp(N) aS dagger V (I) and for all integers i a (c) 3/4 0, the R-modules Ext (R) (i) (N,M) are of finite length, if and only if, for all finitely generated R-modules N with Supp(N) aS dagger V (I) and for all integers i a (c) 3/4 0, the R-modules Ext (R) (i) (M,N) are of finite length.