Every algebraic extension of a finite field is a finite extension. True or False?
113175
Why is the algebraic closure of a finite field countable?
16643
A slick proof that a field which is finitely generated as a ring is finite
153622
Are intermediate rings of finitely generated ring extensions also finitely generated?
68753
Elements in finite field extensions
74663
Is $\mathbb{R}$ an algebraic extension of some proper subfield?
93111
Finiteness of the Algebraic Closure
137373
Real Cyclic Extensions of $\mathbb Q$ of given degree
48093
Irreducible polynomial in field extension
119305
Is the splitting field equal to the quotient $k[x]/(f(x))$ for finite fields?
80879
Can a quotient field ever be finitely generated as an algebra?
142336
Why does the integral domain "being trapped between a finite field extension" implies that it is a field?
116594
Finite fields are isomorphic
131143
Homomorphism extensions over finite ring extensions
79450
For field extensions $F\subsetneq K \subset F(x)$, $x$ is algebraic over $K$
69935
Field extensions of finite degree and primitive elements
111347
Finding an example of field extensions satisfying certain properties
131460
Example of finite field extension where root not separable