Is every subring of a principal ideal ring also a principal ideal ring?
119866
Subring of PID is also a PID?
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
41629
Structure of ideals in the product of two rings
49948
If every ideal is principal show the same is true for the image of a homomorphism.
146801
Primary decomposition of an ideal
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
104789
How to tell an ideal of integer polynomial ring is principal?
37410
Example of a ring with an infinite inclusion chain of ideals
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
31585
Primary ideals of $\mathbb{Z}$
105887
Ring and Subring with different Identities
126672
Product of principal ideals: $(a)\cdot (b) = (a b)$
52966
Rings, ideals and units-proof
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
121986
Do the Laurent polynomials over $\mathbb{Z}$ form a principal ideal domain?
65536
Finitely generated ideals in a Boolean ring are principal, why?
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )