COMPLETIONS OF NOETHERIAN PI-RINGS

Let R be a left noetherian p.i. ring and M a maximal (semimaximal) ideal in R satisfying ∩iMi = {0}. It is proven that R ̂&z.tbnd;limi R Mi, the completion of R with respect to {Mi}, is left noetherian, settling affirmatively a conjecture of Goldie [G]. However, usually R ̂ is neither left nor right flat over R and height (M) ≠ height( M ̂). © 1990.