Showing the factor ring $\mathbb Z[x]/\langle x^2 + 1\rangle$ is isomorphic to the Gaussian integers.
33781
Is $\mathbb{Z}[x]/(x^2+1)$ isomorphic to $\mathbb{Z}[i]$?
102721
Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
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
30401
Determining the structure of the quotient ring $\mathbb{Z}[x]/(x^2+3,p)$
83001
Easier way to show $(\mathbb{Z}/(n))[x]$ and $\mathbb{Z}[x] / (n)$ are isomorphic
52081
Why is not the ring $\mathbb{Z}[2\sqrt{2}]$ a unique factorization domain?
90433
Isomorphisms between $(\mathbb Z_4,+)$ and $(U_5,*)$
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
109610
Is $\mathbb{R}[X]/(P)$ isomorphic to $\mathbb C$ for every irreducible polynomial $P$ of degree $2?$
40114
Factor into irreducibles in $\mathbb{Z}[\omega]$ (Eisenstein Integers).
144789
identify the ring $\mathbb{Z}[x]/(2x-1)$
1719
Ideals in the ring of Gaussian integers
141124
Automorphisms of the ring $\Bbb Z[x]$ of polynomials with integer coefficients
42552
Localisation is isomorphic to a quotient of polynomial ring
108775
Identify the ring $\mathbb {Z}[i]/(2 + i) $