A characterization of cominimax and weakly cofinite modules

摘要

Let R be a commutative Noetherian ring andIbe an ideal of R. Let Mbe 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 superset of I with dim R/J = 0. Moreover, it is shown that M is I-weakly cofinite if and only if there is an ideal J superset of I such that V(J) is a finite set and M is (I,V(J))-cofinite.