Artinian integral domains are fields.
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
67699
Integral domain that is integrally closed, one-dimensional and not noetherian
32839
Example of integral domain with infinitely ascending chain of ideals.
78950
Does this map extend to a unique automorphism of the polynomial ring of an integral domain?
84386
Domain strictly contained in the intersection of localizations at the primes of height one
98540
If $F[x]$ is a principal domain does $F$ have to be necessarily a field?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
153589
Integral basis of an extension of number fields
74139
Subrings of integral domains have the same identity element.
551
Why is a finite integral domain always field?
112099
Polynomial ring with integral coefficients is integral
135152
Non-UFD integral domain such that prime is equivalent to irreducible?
94579
$\mathbb{Q}[x,y]/\langle x^2+y^2-1 \rangle$ is an integral domain, and its field of fractions is isomorphic to $\mathbb Q(t)$
80295
Field extensions and algebraic/transcendental elements
58532
If $M$ is an Artinian $R$-module then $R/\mbox{ann}(M)$ is an Artinian ring?