Proof that $M \;$is a field
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
89782
To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
145140
Subfield of $\mathbb{Q}(\sqrt[n]{a})$
94429
Alternative methods to prove that $Z_m$ is a field under addition and multiplication $\bmod\ m$ iff $m$ is a prime
58424
If $A$ an integral domain contains a field $K$ and $A$ over $K$ is a finite-dimensional vector space, then $A$ is a field.
6410
Prove that $(ma, mb) = |m|(a, b)\ $ [GCD & LCM Distributive Law]
76496
Showing that every field is an integral domain.
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
134896
Enlightening proof that the algebraic numbers form a field
138911
Is $\mathbb R^2$ a field?
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
133561
show that if $K$ is a field then $K[x]$ is principal
6855
Subfields of finite fields
93328
$\mathbb{F}_p[X]/(X^2+X+1)$ is a field iff $p \equiv 2 \bmod 3$
4401
Constructive proof that algebraic numbers form a field
122415
How to show every field is a Euclidean Domain.
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 $K[x]$.