Let $R=\mathbb{Z}[i]/(3+i)$. Why is this a ring and show that $|R|=10$.
6121
Quotient ring of Gaussian integers
52454
If $x^3 =x$ then $6x=0$ in a ring
91962
In a ring $a*a=0$ then $a+a=0$
31933
$x^2 = 1$ in the ring $\mathbb{Z}/n \mathbb{Z}$
127978
Another point of view that $\mathbb{Z}/m\mathbb{Z} \times\mathbb{Z}/n\mathbb{Z}$ is cyclic.
154613
Showing a set of fractions is a ring
52966
Rings, ideals and units-proof
17895
Let $R$ be a commutative ring with 1 then why does $a\in N(R) \Rightarrow 1+a\in U(R)$?
78118
Algebraically, why is $\mathbb{Z}[i]/(i + 1)$ isomorphic to $\mathbb{Z}_{2}$?
34668
Find all rings $R$ satisfying $\mathbb Z \subset R \subset \mathbb Z[\frac {1}{2}]$
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
14191
How many elements does the ring $ℤ[X]/(X^2-3,2X-4)$ have? Describe the structure of this ring.
111824
Sum of nilpotent and element is a unit in ring?
116651
Show for any simple ring without identity, R, that R is a division ring.
87078
Prove the following set is an ideal of the ring $Z[x]$
102721
Number of elements in the ring $\mathbb Z [i]/\langle 2+2i\rangle$
118299
Show that $(\mathbb{Z}[x]/(x^{n+1}))^{\times}\cong \mathbb{Z}/2\mathbb{Z}\times\Pi_{i=1}^n\mathbb{Z}$