Show that the ring $\mathbb{Z}[i]/n\mathbb{Z}[i]$ is finite.
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
133019
Nilpotent elements in $\mathbb Z_n$
124151
Finite ring extension and number of maximal ideals
17239
Find all ideals of ${\mathbb{Z}_n}$
116526
Finite ring has only zero divisors and units
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
157585
Structure theorem of finite rings
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
14055
How to show that a finite commutative ring without zero divisors is a field?
51428
Do these two observations suffice to show that a finite boolean ring must be of the form $\mathbb{Z}_2\times\cdots\times\mathbb{Z}_2$?
5699
The number of ring homomorphisms from $\mathbb{Z}_m$ to $\mathbb{Z}_n$
151928
How to prove that $N\setminus A$ is finite?
75970
$\mathbb Z[1/2]$ is not finitely generated?
129302
Proving whether ideals are prime in $\mathbb{Z}[\sqrt{-5}]$
155168
Is the collection of finite subsets of $\mathbb{Z}$ countable?