Show that ideal $(X,Y)\subset \mathbb{R}[X,Y]$ is not invertible
36078
Example of a non invertible fractional ideal
50908
Showing a Ring and an Ideal are equal
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
96787
Why is the arbitrary sum, but not the arbitrary intersection, of ideals an ideal?
156457
Show that $K[x,xy,xy^2,\dots]$ is not Noetherian
149973
Showing the following coordinate rings are not isomorphic
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
47251
Non-compactness of $\mathbb{R}$ with the cocountable topology
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
3296
Proof That $\mathbb{R} \setminus \mathbb{Q}$ Is Not an $F_{\sigma}$ Set
85586
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
35569
Prove that $[0,1]$ isn't homeomorphic to $\mathbb{R}$
114198
Showing that $y$ is irreducible in $\mathbb R[x,y]/(x^2+y^2-1)$.
21599
$(0,1)$ is an open subset of $\mathbb{R}$ but not of $\mathbb{R}^2$, when we think of $\mathbb{R}$ as the x-axis in $\mathbb{R}^2$. Prove this.
21946
What do prime ideals in $k[x,y]$ look like?
140553
An ideal which is not finitely generated