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(IbRJ +AnnbRJ M) = JbR J , where J := \m2SuppM m and bRJdenotes the J-adic comletion of R.