Show that α^2 is algebraic over K (Field extension)
60348
How do I prove $F(a)=F(a^2)?$
99516
Show $\mathbb{Q}[\sqrt[3]{2}]$ is a field by rationalizing
133561
show that if $K$ is a field then $K[x]$ is principal
57283
Extending Homomorphism into Algebraically Closed Field
58811
Every algebraic extension of a perfect field is separable and perfect
66355
A sufficient condition for irreducibility of a polynomial in an extension field.
147069
Intersection of field extensions
31142
Why does $K \leadsto K(X)$ preserve the degree of field extensions?
122050
Algebraic extension of perfect field in which every polynomial has a root is algebraically closed
50668
Show that $\mathbb{Q}(\sqrt2, \sqrt[3]2)$ is a primitive field extension of $\mathbb{Q}$.
48093
Irreducible polynomial in field extension
61429
Is the algebraic closure of a $p$-adic field complete
92677
Infinite algebraic extension of a finite field
148310
Showing rational numbers are algebraic
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
46565
Show that $\mathbb{Q}(\sqrt{2})$ is a field.
146446
Infinite Degree Algebraic Field Extensions