The ideal generated by $x^m-1$ and $x^n-1$ in $\mathbb{Z}[X]$ is principal.
6012
Prove that $\gcd(a^n - 1, a^m - 1) = a^{\gcd(n, m)} - 1$
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
81743
Prime ideals in $C[0,1]$
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
93929
The height of a principal prime ideal
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
104789
How to tell an ideal of integer polynomial ring is principal?
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?
155745
Ideals of $\mathbb{Z}[X]$
49436
Show that the ring of all rational numbers, which when written in simplest form has an odd denominator, is a principal ideal domain.
146801
Primary decomposition of an ideal
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
89056
Intuitive understanding of ideal $I = (x+1,x^2+1)$ and the quotient $\Bbb Z[x]/I$
149203
Symbolic power of a prime ideal is primary