Prove that an ideal in $k[x,y]$ is a prime ideal
2043
$X^n-Y^m$ is irreducible in $\Bbb{C}[X,Y]$ iff $\gcd(n,m)=1$
102341
Primary decomposition of a monomial ideal
146304
prove $(n)$ prime ideal of $\mathbb{Z}$ iff $n$ is prime or zero
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module
108380
Assume $P$ is a prime ideal s.t. $K \subset P$, show $f(P)$ is a prime ideal
120181
The ideal generated by $2$ and $ x$ in $\mathbb{Z}[x]$
80397
Show that this set of polynomials is ideal in F[x]
52966
Rings, ideals and units-proof
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
36150
Ideal in a ring of continuous functions
19883
Prime ideals of the matrix ring
106550
The bijection between homogeneous prime ideals of $S_f$ and prime ideals of $(S_f)_0$
116000
Prove that prime ideals of a finite ring are maximal
56800
Intersection of prime ideals
111287
number of prime ideals in algebraic integers
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
15904
Prime ideal and nilpotent elements