$k[x]/(x^2)$ has only one prime ideal
45684
Is quotient of a ring by a power of a maximal ideal local?
7833
Ideal and minimal polynomial
75558
Counter-example for prime ideals in a non commutative ring.
145594
Splitting of prime ideals in algebraic extensions
135682
Are distinct prime ideals in a ring always coprime? If not, then when are they?
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
116000
Prove that prime ideals of a finite ring are maximal
83050
Show that $P[x]+\langle x\rangle $ is a prime ideal of $R[x]$.
81743
Prime ideals in $C[0,1]$
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
131497
Maximal ideal not containing the set of powers of an element is prime
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
70712
How to prove that $k[x, xy, xy^2, \dotsc]$ is not noetherian?
20296
The ideal $I= \langle x,y \rangle\subset k[x,y]$ is not principal