Proving that $D^{-1}\mathbb{Z}\cong \mathbb{Z}[x]/(px-1)$
42552
Localisation is isomorphic to a quotient of polynomial ring
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
4648
Proving that $\mathbb{Z}_m\oplus \mathbb{Z}_n \cong \mathbb{Z}_d\oplus \mathbb{Z}_l $ as groups, where $l=\mathrm{lcm}(m,n)$ and $d=\gcd(m,n)$
60208
Proof of property of abelian group
93621
Prove that $\mathbb{Z}[\omega]$ is an integral domain
46147
Proving $(\forall a\in\mathbb{Z^+})(m\in\mathbb{Z^+}\to a^m\equiv a^{m-\phi(m)}\pmod{m})$
92703
Proving that $\mathbb{Z}[x]$ and $\mathbb{Q}[x]$ are not isomorphic.
145752
Aut $\mathbb Z_p\simeq \mathbb Z_{p-1}$
139595
Show that $(l_1)^* \cong l_{\infty}$
1020
Proving that $\mathbb{Z}[\sqrt{2}]$ is a Euclidean domain
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
55673
Alternate proof that $\exists\ x \in \Bbb{Z}$ such that $ \gcd (a+bx,c) = 1$?
122741
$x^2$ is congruent to $-1 \bmod p$
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
55902
Show $R[x]/(x)\cong R$
120594
$\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
154945
$|px^2+qx+r|\le1$ for all $x$ in $[-1; 1]$, show that $|rx^2+qx+p|\le2$ for all $x$ in $[-1; 1]$