Show an ideal is not principal in $\mathbb{F}[x,y]$
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal
31585
Primary ideals of $\mathbb{Z}$
27167
Ideals in $F[x]$ and Euclidean domains are generated by any element of minimal degree
61383
How do I see that every left ideal of a square matrix ring over a field is principal?
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
3604
If F is a field, then $F[x,y]$ is a Principal Ideal Domain?
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
17991
Nonconstant polynomials do not generate maximal ideals in $\mathbb Z[x]$
110022
Showing prime and maximal ideal
50908
Showing a Ring and an Ideal are equal
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
90314
Maximal ideals in $R[x]$
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
138168
Prove: The pre-image of an ideal is an ideal.
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
80961
Prove that a commutative ring $F$ is a field iff $F[x]$ is a Principal Ideal Domain
87382
Non-invertible elements form an ideal