ABSTRACT Let R be a commutative Noetherian ring and I be an ideal of R. Let M be an arbitrary R-module. In this paper we establish some results concerning the cofiniteness properties of modules. It is shown that, M is I-cominimax if and only if there is an ideal J I with dimR=J 0 such that M is ðI, VðJÞÞ-cofinite and the R-module Ext iR ðR=J, MÞ is finitely generated, for each i ! 0: Moreover, it is shown that M is I-weakly cofinite if and only if there is an ideal J I such that V(J) is a finite set and M is ðI, VðJÞÞ-cofinite.
