Prove the Krull dimension of coordinate ring of $y^2=x^3$ is $1$.
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
85525
Prove that $x^3+x+1$ splits in $Z_2[x]/(x^3+x+1)$
44453
Prove that the normalisation of $A=k[X,Y]/(Y^2-X^2-X^3)$ is $k[t]$ where $t=Y/X$ (Reid, Exercise 4.5)
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
46211
$(K[x,y,z]/(x^2+y^3+z^7))_{(x,y,z)}$ is a UFD.
27096
Hilbert polynomial of an hypersurface in projective space
77361
How to prove $|H|[K:K \cap (g^{-1}Hg)]=|K|[H:H \cap (gKg^{-1})]$?
115541
Subrings of polynomial rings over the complex plane
46622
Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.
133884
A proof using Yoneda lemma
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
109288
Prove that $x^3+y^3+z^3-3xyz=1$ defines a surface of revolution
26780
Dimension of cone of projective variety
63192
A chain ring with Krull dimension greater than one
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
24224
How to prove the ring of Laurent polynomials over a field is a principal ideal domain?