How to show $\langle 7\rangle$ is a prime ideal of $\Bbb Z[x]$
37929
Classification of prime ideals of $\mathbb{Z}[X]$
44496
Norm $N$ on $\Bbb Z[\sqrt d]$ is multiplicative, $N(x)$ prime $\Rightarrow x$ irreducible
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.
33245
Show that every ideal of the ring $\mathbb Z$ is principal
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
97258
Give $\ker(\phi)$ for $\phi: \mathbb{Z} \to \mathbb{Z_7}$ such that $\phi(1)=4$
111996
Maximal and Prime Ideal in Z
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
120594
$\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
3711
Finding the intermediate fields of $\Bbb{Q}(\zeta_7)$.
124438
Find $|(\mathbb{Z} \oplus \mathbb{Z}) / \langle(3,6)\rangle|$ and determine if its cyclic
112045
A property of minimal prime ideal
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
70856
Construct ideals in $\mathbb Z[x]$ with a given least number of generators
15904
Prime ideal and nilpotent elements
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$