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Is there a classification of the algebraically closed fields that have maximal proper subfields ? And if an algebraically closed field has a maximal proper subfield, is that subfield unique ? Summarizing the answers, an algebraically closed field has a maximal subfield if and only if its characteristic is zero and such a maximal subfield is never unique. |
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Algebraically closed fields with proper maximal subfieldsIs there a classification of the algebraically closed fields that have maximal proper subfields ? And if an algebraically closed field has a maximal proper subfield, is that subfield unique ?
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