Proving that any finite integral domain is a field.
551
Why is a finite integral domain always field?
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
16984
Finite extension of domains : preimage of non-zero ideal is non-zero?
128550
Algebraic field extension and intermediate integral domain
10111
Prove or disprove that Q[√2] is a field
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
141410
Injective integral domains are fields
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
116594
Finite fields are isomorphic
74139
Subrings of integral domains have the same identity element.
92677
Infinite algebraic extension of a finite field
90599
Trouble with proving $A$ is an integrally closed domain $\Rightarrow$ $A[t]$ is integrally closed domain
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
47474
Proving $|f(z)|$ is constant on the boundary of a domain implies $f$ is a constant function
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
78626
Let $R$ be a commutative ring. If $R[X]$ is a principal ideal domain, then $R$ is a field.