Zero-divisors in completions of non-commutative rings (Q1802793)

An example is constructed of a Noetherian ring \(R\) with the following properties: there is a maximal ideal \(M\) of \(R\) such that \(R/M\) is Artinian and the intersection of the powers of \(M\) is 0; and there is a regular normal element \(x\) of \(R\) such that \(x\) becomes a zero divisor in the completion of \(R\) at \(M\). This contrasts with the fact that if \(R\) is commutative then \(x\) remains regular in the completion.