Showing $\mathbb{Z}[i]/\langle 3 + 4i \rangle \cong \mathbb{Z}/25\mathbb{Z}$: how to guess?
54585
Order of some quotient ring of Gaussian integers
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
123482
How to compute $\mathbb{Z}_n^*$, the unit group of the integers modulo $n$?
93703
Groups of units of $\mathbb{Z}\left[\frac{1+\sqrt{-3}}{2}\right]$
91622
Help with proof that $\mathbb Z[i]/\langle 1 - i \rangle$ is a field.
98284
show $\Bbb Z_6 \cong \Bbb Z_3 \times \Bbb Z_2 $.
52483
Showing that $(m)\cap (n)=(\operatorname{lcm}(m,n))$ and $(m)+(n)=(\gcd(m,n))$ for any $m,n\in\mathbb{Z}$
33025
What is the order of $(\mathbb{Z} \oplus \mathbb{Z})/ \langle (2,2) \rangle$ and is it cyclic?
68915
What are the units in $\mathbb{Z}[\root 3 \of 2]$?
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
12110
How are $2\mathbb{Z}\ncong3\mathbb{Z}$ different as rings?
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
145112
Show that the multiplicative group $(\mathbb{Z}/p\mathbb{Z})^*$ is cyclic
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
30752
Proof of $(\mathbb{Z}/m\mathbb{Z}) \otimes_\mathbb{Z} (\mathbb{Z} / n \mathbb{Z}) \cong \mathbb{Z}/ \gcd(m,n)\mathbb{Z}$
145279
Compute the (multiplicative) inverse of $4x+3$ in the field $\frac {\Bbb F_{11}[x]}{\langle x^2+1 \rangle}$?