Prove that the ideal of $\mathbb{R}[x]$ generated by $x^3-x^2+x-1$ and $x^4+3x^2+2$ is a prime ideal
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
7833
Ideal and minimal polynomial
110022
Showing prime and maximal ideal
53575
Describe $R=\mathbb{Z}[X]/(X^2-3,2X+4)$
40975
Quotient of the ring of integers of a number field by a prime ideal
138114
Proving the quotient of a principal ideal domain by a prime ideal is again a principal ideal domain
17239
Find all ideals of ${\mathbb{Z}_n}$
87078
Prove the following set is an ideal of the ring $Z[x]$
142212
Let $q$ be a prime congruent to 3 mod 4, prove the quotient ring $\mathbb{Z}[i]/(q)$ is a field with $q^2$ elements
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
79535
Prove that $R$ is a commutative ring if $x^3=x$
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
90314
Maximal ideals in $R[x]$
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
81743
Prime ideals in $C[0,1]$