Show that every finite integral domain is a field
551
Why is a finite integral domain always field?
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
122415
How to show every field is a Euclidean Domain.
146470
Show $\mathbb{Z}[\sqrt{6}]$ is a Euclidean domain
31049
If $p$ is an irreducible element of an integral domain $D$, and if $e$ belongs to $D^\ast$ prove that $ep$ is also ireducible
33645
Proving that an integral domain has at most two elements that satisfy the equation $x^2 = 1$.
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
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.
74681
A finite extension with finitely many intermediate fields is simple
111444
Is any finite-dimensional extension of a field, say $F$, algebraic and finitely generated?
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
139463
Commutative integral domain does not finitely generate its field of fractions
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
98577
Show that the set $\mathbb{Q}(\sqrt{p})=\{a+b\sqrt{p}; a,b,p\in\mathbb{Q},\sqrt{p}\notin \mathbb{Q}\}$ is a field
97902
In a integral domain every prime element is irreducible