finite integral domain algebras are division algebras
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
151794
Can an ideal in a commutative integral domain be its own square?
114267
If $S$ is a finitely generated graded algebra over $S_0$, $S_{(f)}$ is finitely generated algebra over $S_0$?
79460
Atiyah-Macdonald, Exercise 8.3: Artinian iff finite k-algebra.
73344
Definition of irreducible polynomial via the units of an integral domain.
132317
linear algebra over a division ring vs. over a field
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
7011
Integral domain with fraction field equal to $\mathbb{R}$
551
Why is a finite integral domain always field?
133636
Is $\mathbb Z[X]/(X^2-1)$ a domain?
112345
In an Integral Domain is it true that $\gcd(ac,ab) = a\gcd(c,b)$?
154530
Rings whose elements are partitioned between units and zero-divisors.
150206
Every finitely generated algebra over a field is a Jacobson ring
18066
Prove that any non-zero-divisor of a finite dimensional algebra has an inverse
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
132193
Why $\Bbb Z$ = (integers) is an integral domain?