Commutative integral domain with d.c.c. is a field
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
139463
Commutative integral domain does not finitely generate its field of fractions
76496
Showing that every field is an integral domain.
124511
The set of algebraic numbers is a field.
14055
How to show that a finite commutative ring without zero divisors is a field?
83009
Showing that $R(x)$ is a proper subset of $R((x))$ if $R$ is a field
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
151018
Proving that any finite integral domain is a field.
23721
Prove that the Gaussian Integer's ring is a Euclidean domain
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
124672
Let $f:R\rightarrow S$ be a ring homomorphism. Prove or disprove: if $f$ is onto and $R$ is an integral domain, then $S$ is an integral domain
25397
Prove $R \times R$ is NOT an integral domain
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain