Abstract
Let R be a prime Goldie ring and (σ,δ) be a skew derivation on R. It is well known that if R is a maximal order, then the Ore extension R[x;σ,δ] is a maximal order. It was a long standing open question that the converse is true or not in case σ≠1 and δ≠0.We give an example of non-maximal order R with a skew derivation (σ,δ) on R (σ≠1,δ≠0) such that R[x;σ,δ] is a maximal order.
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