Pseudo algebraically closed field
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The field K is pseudo algebraically closed if one of the following equivalent conditions holds:
- Each absolutely irreducible variety V defined over K has a K-rational point.
- Each absolutely irreducible polynomial
![f\in K[T_1,T_2,\cdots ,T_r,X]](../../../math/a/7/7/a7762bd644a90b7dff9a4642a625a207.png)
with 
and for each ![0\not =g\in K[T_1,T_2,\cdots ,T_r,X]](../../../math/8/5/0/85038266950f95b09d9465bd8c874cda.png)
there exists 
such that 
and 
. - Each absolutely irreducible polynomial
![f\in K[T,X]](../../../math/d/9/5/d95523c0fbe3943614f0f33ad71af0db.png)
has infinitely many K-rational points. - If R is a finitely generated integral domain over K with quotient field which is regular over K, then there exist a homomorphism
such that h(a) = a for each 
