Abstract
It has long been known that an integral domain A can be Noetherian while its integral closure A′ is not. However, when Heinzer asked whether A′ can have an infinitely generated maximal ideal, the question went unanswered. In this article, a local Noetherian domain A is constructed with the property that A′ has an infinitely generated maximal ideal. Moreover, the completion of A′ is not Noetherian. It had not previously been shown that this can happen.
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