Quick proof that every finite integral domain is a field.
551
Why is a finite integral domain always field?
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
93118
How to show that if two integral domains are isomorphic, then their corresponding field of quotients are isomorphic?
119999
A property of every real polynomial.
97902
In a integral domain every prime element is irreducible
124511
The set of algebraic numbers is a field.
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.
150239
In an integral domain every non-zero prime ideal is invertible implies every non-zero proper ideal is invertible.
73344
Definition of irreducible polynomial via the units of an integral domain.
74139
Subrings of integral domains have the same identity element.
98544
Prove that in any GCD domain every irreducible element is prime
146617
A complete picture of the lattice of subfields for a cyclotomic extension over $\mathbb{Q}$.
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
16984
Finite extension of domains : preimage of non-zero ideal is non-zero?
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
27021
Show that $Q[\sqrt3]$ is a field
138911
Is $\mathbb R^2$ a field?