Prove that $\mathbb{Z}[i]/\langle 1+i \rangle \cong \mathbb{Z}/2\mathbb{Z}$
6121
Quotient ring of Gaussian integers
132725
Is $\mathbb{Z}/\langle n\rangle$ cyclic and of order $n$?
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
61292
How to know which elements are in the Quotient Ring $\mathbb{Z}[x]/\langle x, 2\rangle$?
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
147564
Why does $(A/I)\otimes_R (B/J)\cong(A\otimes_R B)/(I\otimes_R 1+1\otimes_R J)$?
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
90437
Let $G = \langle a\rangle$ a cyclic group of order m. Prove that G is isomorphic with $Z_m$.
89215
How to describe the quotient group $\mathbb{Z} \times \mathbb{Z} / \langle (1, 2) \rangle$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
152932
Proof: $\det\pmatrix{\langle v_i , v_j \rangle}\neq0$ $\iff \{v_1,\dots,v_n\}~\text{l.i.}$
87946
Proving that the unities of a ring form a group under multiplication
54267
Field of fractions of $\mathbb{Q}[x,y]/\langle x^2+y^2-1\rangle$
147968
Calculate the Factor Group $(\mathbb{Z}_4 \times \mathbb{Z}_6)/\langle(0,2)\rangle$