Is it true that the order of any quotient ring $\mathbb Z[i]/\langle a+ib \rangle $ is $a^2+b^2$ ? (where not both $a,b$ are zero)
54585
Order of some quotient ring of Gaussian integers
20097
Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
104034
Is $\le$ defined by $\langle 𝑥_1, 𝑦_1 \rangle \le \langle 𝑥_2, 𝑦_2 \rangle$, if $𝑥_1 \le 𝑥_2 \land𝑦_1 \ge 𝑦_2$ a linear order?
41731
Question about the order of the product of two elements in an abelian group
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
124230
What is $\operatorname{Hom}_\mathbb{Z}(\mathbb{Q}/\mathbb{Z},\mathbb{Q}/\mathbb{Z})$?
93773
How many elements are in the quotient ring $\frac{\mathbb Z_3[x]}{\langle 2x^3+ x+1\rangle} $
92517
Easy way to show that $\mathbb{Z}[\sqrt[3]{2}]$ is the ring of integers of $\mathbb{Q}[\sqrt[3]{2}]$
129750
Order of $SL_2(\mathbb{Z}/ n\mathbb{Z})$
37061
The order of $ab$ when $a,b$ commute
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
106911
Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
15387
Order of $GL(n, \mathbb Z_p)$