Examples
- Any algebraically closed field is quasi-algebraically closed. In fact, any homogeneous polynomial in at least two variables over an algebraically closed field has a non-trivial zero.
- Any finite field is quasi-algebraically closed by the Chevalley–Warning theorem.
- Algebraic function fields over algebraically closed fields are quasi-algebraically closed by Tsen's theorem.
- The maximal unramified extension of a complete field with a discrete valuation and a perfect residue field is quasi-algebraically closed.
- A complete field with a discrete valuation and an algebraically closed residue field is quasi-algebraically closed by a result of Lang.
- A pseudo algebraically closed field of characteristic zero is quasi-algebraically closed.
Read more about this topic: Quasi-algebraically Closed Field
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