SOME RESULTS ON THE ARTINIAN COFINITE MODULES

Let I be an ideal of a commutative Noetherian ring R and M be a non-zero Artinian R-module with support contained in V(I). In this paper it is shown that M is I-cofinite if and only if \Rad(I\widehat{R}^J+\Ann_{\widehat{R}^J}M)=J\widehat{R}^J, where J:=\cap_{\m\in \Supp M}\m and \widehat{R}^J denotes the J-adic comletion of R.

کلیدواژه ها:

Artinian module ، attached prime ideal ، cofinite module ، Noetherian Ring