Prime element of integral domain is irreducible. Counterexample of inverse.
73702
What are examples of irreducible but not prime elements?
64878
Is this polynomial irreducible in $\mathbb{Q}$?
121658
$x^2+y^2-1$ irreducible in $\mathbb{Q}[x,y]$?
139463
Commutative integral domain does not finitely generate its field of fractions
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
87101
Irreducible but not prime in $K[X,Y]/(X^2-Y^3)$
551
Why is a finite integral domain always field?
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
90533
Show that if $p(x)$ is reducible in $F[x]$, then $F[x]/(p(x))$ is not an integral domain.
120147
For what prime numbers $p$ is $x^2+x+1$ irreducible in $\mathbb{F}_p[X]$
138851
Euclid's Lemma in a PID: irreducibles are prime: $ \pi\mid ab\Rightarrow \pi\mid a\,$ or $\pi\mid b$
41693
Use irreducible fibers to show $X$ is irreducible
38364
Showing that $x^n -2$ is irreducible in $\mathbb{Q}[X]$
123024
A Noetherian integral domain is a UFD iff $(f):(g)$ is principal
22544
Let R be a commutative ring, and let P be a prime ideal of R. Suppose that P has no nontrivial zero divisors in it. Show that R is an integral domain.
8977
Showing $x^{5}-ax-1\in\mathbb{Z}[x]$ is irreducible