Show that $(x)$ is a prime ideal in $\mathbb{Z}[x]$ (the polynomials with integer coefs) which is not maximal.
92519
ideal behind Maximal ideals are Prime ideals
112045
A property of minimal prime ideal
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
140553
An ideal which is not finitely generated
67203
Complement of maximal multiplicative set is a prime ideal
70856
Construct ideals in $\mathbb Z[x]$ with a given least number of generators
151829
Why are maximal ideals prime?
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.
111996
Maximal and Prime Ideal in Z
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
81743
Prime ideals in $C[0,1]$
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
43889
Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$
23099
Verifying that the ideal $(x^3-y^2)$ is prime
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set