Example of a primary ideal that it's not prime
31585
Primary ideals of $\mathbb{Z}$
37929
Classification of prime ideals of $\mathbb{Z}[X]$
81743
Prime ideals in $C[0,1]$
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
36078
Example of a non invertible fractional ideal
148434
Ring where irreducibles are primes which is not an UFD
111935
Irreducible but not prime
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
69710
Is it true that an ideal is primary iff its radical is prime?
15128
Example of non-decomposable ideal
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
120496
Examples of Non-Noetherian Valuation Rings
252
Why doesn't $0$ being a prime ideal in $\mathbb Z$ imply that $0$ is a prime number?
108896
Prime ideal in a polynomial ring over an integrally closed domain
25764
Example of a ring such that $R^2\simeq R^3$, but $R\not\simeq R^2$ (as $R$-modules)
104789
How to tell an ideal of integer polynomial ring is principal?
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)