Show that there are finitely many different principal ideals
43103
Unique factorization domain and principal ideals
104789
How to tell an ideal of integer polynomial ring is principal?
37929
Classification of prime ideals of $\mathbb{Z}[X]$
138672
Finding Ideals in $\begin{bmatrix} \mathbb{Q} & \mathbb{Q}\\ 0 & 0 \end{bmatrix}$
65536
Finitely generated ideals in a Boolean ring are principal, why?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
60223
Two principal ideals coincide if and only if their generators are associated
50445
Explaining the product of two ideals
111129
Show that $[K:F]_s = [K:L]_s [L:F]_s$ and $[K:F]_i = [K:L]_i [L:F]_i$.
133561
show that if $K$ is a field then $K[x]$ is principal
138882
A prime poset of ideals
145351
Ring of formal power series over a principal ideal domain is a unique factorisation domain
89313
Maximal ideals of polynomial rings in infinitely many variables
63447
Prove that the kernel of a homomorphism is a principal ideal. (Artin, Exercise 9.13)
56800
Intersection of prime ideals
81743
Prime ideals in $C[0,1]$
60391
Ideal Generated by Three Elements in Polynomial Ring