$F(x)$ versus $F[x]$ where $F$ is a field
51612
Question About Notation In Field Theory $F(x)$ vs. $F[x]$
21954
A question about $f(x)\equiv 0$
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
78561
Algebraic field extensions: Why $k(\alpha)=k[\alpha]$.
85096
Let $K$ be a field and $f(x)\in K[x]$. Prove that $K[x]/(f(x))$ is a field if and only if $f(x)$ is irreducible in $K[x]$.
96539
is $f$ constant or dilation
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
6855
Subfields of finite fields
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
33586
Prove the field of fractions of $F[[x]]$ is the ring $F((x))$ of formal Laurent series.
138424
Scalar field Derivative. Real vs Complex
77074
If $ f(f(f(x)))=x$, does$ f(x)=x$ necessarily follow?
41018
What is the main difference between a vector space and a field?
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
149849
Let $F$ be a field and $f: \mathbb{Z} \to F$ be a ring epimorphism.
143219
If a field $F$ is an algebraic extension of a field $K$ then $(F:K)=(F(x):K(x))$