In an integral domain $R$ associates of an irreducible element are irreducible.
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
17670
If $p\in R[X_1,\dots,X_n]$ is irreducible, is it still irreducible in $R[X_1,\dots,X_n,\dots,X_N]$?
120673
Irreducible fibers of a closed subset implies irreducibility
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
62951
Is there a more direct way of proving that this ring is an integral domain?
96132
$R$ integral domain : $u\in R^*, a \text{ is prime} \iff au \text{ is prime}$
551
Why is a finite integral domain always field?
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
112371
Computing irreducible components of algebraic set
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
132289
Associates in Integral Domain
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
62134
Show that if $ R $ is an integral domain then a polynomial in $ R[X] $ of degree $ d $ can have at most $ d $ roots
10627
When is $X^n-a$ is irreducible over F?
108767
Irreducible Components of the Prime Spectrum of a Quotient Ring and Primary Decomposition
13983
Show that If $R[X]$ is Euclidean domain then $R$ is a field