Why does every non-zero ideal in $\mathcal{O}_K$ is of finite index?
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
109691
When are kernels of homomorphisms on $\mathbb{Z}[x]$ principal ideals, and what does this have to do with Gauss's lemma?
21946
What do prime ideals in $k[x,y]$ look like?
65536
Finitely generated ideals in a Boolean ring are principal, why?
117536
Why is the localization at a prime ideal a local ring?
140553
An ideal which is not finitely generated
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
74537
Maximal Ideals in $K[y]$
53469
C(0, 1) has infinitely many prime ideals not of the form Mp
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
64408
Subgroup of $\mathbb{Q}$ with finite index
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
34807
Localization at finitely many minimal prime ideals
13901
Finitely many prime ideals lying over $\mathfrak{p}$
15137
Does $IJ=IK\implies J=K$ always hold for integral domain and finitely generated nonzero ideal $I$?