Elements of finite field extensions
55492
Existence of $f'\in F$ such that $f^{[G:F]}=(f')^n$ for finite extension $F\subset G$
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
120215
Sum of elements of a finite field
16643
A slick proof that a field which is finitely generated as a ring is finite
111347
Finding an example of field extensions satisfying certain properties
49150
Subscript R notation for the finite fields
129476
The trace map in a finite field.
82328
Constructing a Galois extension field with Galois group $S_n$
48093
Irreducible polynomial in field extension
86877
Let $F$ be a Galois extension over $\mathbb{Q}$ with $[F:\mathbb{Q}]=2^n$, then all elements in $F$ are constructible
16147
Generic Element of Compositum of Two Fields
60212
algebraic element over a field
139499
The algebraic closure of a finite field and its Galois group
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
19511
Is the sub-field of algebraic elements of a field extension of $K$ containing roots of polynomials over $K$ algebraically closed?
41815
Galois extension of intersection of fields
83586
Finite fields and primitive elements