Why is $\pi$ irreducible in $\mathbb{Z}[i]$?
97902
In a integral domain every prime element is irreducible
51221
Is $x^3-9$ irreducible over the integers mod 31?
101637
Let $R$ be an integral domain. If $x \in R$ is prime, then $x$ is irreducible.
158182
Let $R = \mathbb{Z} + x\mathbb{Q}[x]$. Find all the irreducibles in $R$.
86807
The units of $\mathbb Z[\sqrt{2}]$
135102
How do the definitions of "irreducible" and "prime" elements differ?
10627
When is $X^n-a$ is irreducible over F?
25471
Irreducibility of $x^n-x-1$ over $\mathbb Q$
46951
For what values of $n > 1$ and a is $x^n - a$ irreducible in $\mathbb Q[x]$?
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
125604
Proof that $\mathbb{Z}$ has no zero divisors
153062
Question about irreducible Gaussian integers
120940
An irreducible polynomial in a subfield of $\mathbb{C}$ has no multiple roots in $\mathbb{C}$
70249
Irreducibility of Polynomials in $k[x,y]$
90144
Show that if $a+bi$ is irreducible over $\mathbb{Z} [i]$ then $a^2 + b^2$ is prime over $\mathbb{Z} $
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.