Show that $\mathbb{Z}[\sqrt{2}]$ is a commutative ring
86807
The units of $\mathbb Z[\sqrt{2}]$
135699
Questions about a commutative ring with exactly three ideals
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
157488
Proving that $k[x,y,z]/(xz - (y^2 + 1))$ is a normal ring.
129162
Show there is a surjective homomorphism from $\mathbb{Z}\ast\mathbb{Z}$ onto $C_2\ast C_3$
107821
The ring of integers of $\mathbf{Q}[i]$
151803
Prove that $R$ is commutative
124564
Prove the ring $a+b\sqrt[3]{2}+c\sqrt[3]{4}$ has inverse and is a field
55900
Is there a ring homomorphism $M_2(\mathbb Z)\to \mathbb Z$?
143831
Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
63478
Is $\mathbb{Q}(\sqrt{2}) \cong \mathbb{Q}(\sqrt{3})$?
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
9794
Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
62183
Find the quotient field of $\mathbb{Z}[\sqrt {2}]$