Let I and J be ideals of a noetherian ring R. The ascending chain of ideals \((I:J)\subset (I:J^ 2)\subset..\). stabilizes. Let \(I:\) denote the limit. (It is not difficult to see that \(I:\) is the intersection of those primary components of I whose associated prime ideal does not contain J.) This paper compares the filtration \(F=\{I^ n:\}\) with the I-adic filtration of R. It asks ''When is the topology on R induced by F equivalent to the I-adic topology ?'' and ''When is the filtration ring \(\sum (I^ n:)t^ n\quad finitely\) generated as a module (or integral) over the Rees ring \(R[It,t^{-1}] ?''\) The answers are given in terms of analytic spread and various sets of associated prime ideals.