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Uriya First
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Characteristic zero field with unique regular Noetherian dense unital subring

Let $F$ be a field. Call a unital subring $R\subset F$ dense if there is no subfield $K\subsetneq F$ such that $R\subset K$.

Is there a characteristic zero field $F$ such that the only regular Noetherian dense unital subring $R\subset F$ is $F$ itself?

divan
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