# Noetherian completion and PI rings

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## Abstract

Let R be a Noetherian PI ring with a two-sided ideal I. Let $$\hat R$$ be the I-adic completion of R. We establish a criterion which determines when $$\hat R$$ is Noetherian, thus answering a question of A. Goldie. As a consequence a question of J. McConnell is also answered.

Original language English 487-506 20 Israel Journal of Mathematics 209 1 https://doi.org/10.1007/s11856-015-1226-0 Published - 1 Sep 2015