Characteristic of an integral domain without unit element must be prime?
92420
Characteristic of  a Non-unital Integral Ring
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
119699
Examples of Cohen-Macaulay integral domains
25397
Prove $R \times R$ is NOT an integral domain
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
74139
Subrings of integral domains have the same identity element.
7011
Integral domain with fraction field equal to $\mathbb{R}$
70047
Is the ideal generated by irreducible element in principal ideal domain maximal?
57669
A proof that $\mathbb{Z}_{p}$ is an integral domain if and only if $p$ is prime.
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
108896
Prime ideal in a polynomial ring over an integrally closed domain
63659
If D is an Integral Domain and has finite characteristic p, prove p is prime.
154239
Can a prime in a Dedekind domain be contained in the union of the other prime ideals?
78380
Dedekind domain with a finite number of prime ideals is principal
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
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