Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
47134
Ideals generated by two elements
7833
Ideal and minimal polynomial
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
94819
Prove that $\frac{\mathbb{C}[x,y]}{\langle x^2-y^2-1\rangle}$ is an integral domain such that all the nonzero prime ideals are maximal.
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
1719
Ideals in the ring of Gaussian integers
157876
If every prime ideal is maximal, what can we say about the ring?
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
31585
Primary ideals of $\mathbb{Z}$
27916
Are the determinantal ideals prime?
464
Prove that the ideal $(X_1-a_1,...,X_n-a_n)$ is maximal in $K[X_1,\dots,X_n]$
28244
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
147871
How do the prime ideals of $\mathbb{Z}_{k}$ look like?
43774
Given distinct maximal ideals $M_1,...,M_n$, is $M_1\cdots M_n$ radical?