Step-by-step proof of principal ideals.
49948
If every ideal is principal show the same is true for the image of a homomorphism.
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
90314
Maximal ideals in $R[x]$
22789
How to determine whether a unique factorization domain is a principal ideal domain?
138752
Prove the Radical of an Ideal is an Ideal
111307
If ideal $I$ of domain $R$ is free $R$-module, then $I$ is principal ideal.
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
76661
Checking the maximality of a principal ideal in $R[x]$
1425
The Chinese Remainder Theorem for Rings.
99198
Principal ideal and free module
122104
Ideal products and calculating with ideals
4240
The proof of Triple Vector Products
120065
Niven’s theorem proof.
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
116943
Proof for maximal ideals in $\mathbb{Z}[x]$