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2 votes
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Can the completion of a local domain which is not a field be a field?

I would like to prove/disprove the following claim: Let $A$ be an equicharacteristic local domain, and denote by $\widehat{A}$ its completion with respect to its maximal ideal. If $\widehat{A}$ is ...
Don's user avatar
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1 vote
2 answers
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Krull-dimension of local domain

Let $(R,{\frak m}_R)$ be a local domain (not necessarily Noetherian). That is, $R$ is integral and ${\frak m}_R$ is the unique maximal ideal of $R$. Suppose that ${\frak m}_R$ is finitely generated. ...
Pierre MATSUMI's user avatar