A finite field is not algebraically closed.
104115
Why are polynomials defined to be "formal" (vs. functions)?
73652
Exhibiting an isomorphism between two finite fields
40663
$a_1 a_1', a_2 a_2', ..., a_n a_n'$ is not a reduced modulo system $\mod p$.
61428
Show that an algebraically closed field must be infinite.
86626
Finite fields, existence of field of order $p^n$,proof help
140553
An ideal which is not finitely generated
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
56171
Is $K(X)$ never algebraically closed?
136422
Two finite fields with the same number of elements are isomorphic
69935
Field extensions of finite degree and primitive elements
151018
Proving that any finite integral domain is a field.
55764
Algebraic closure of $\mathbb F_p$
140106
How to prove a finite field is not ordered?
131460
Example of finite field extension where root not separable
97004
Algebraic closure not even finitely generated over base field
129227
An example of neither open nor closed set