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Uriya First
Uriya First
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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 F$$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?

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

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

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?

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divan
divan
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Characteristic zero field without properwith unique regular Noetherian dense unital subringssubring

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divan
divan
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Characteristic zero field without proper regular Noetherian dense unital subrings

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

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