If $R$ is a ring of integers, $R/I$ is finite
138459
Norm and Algebraic Integers
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
50908
Showing a Ring and an Ideal are equal
9806
$M$ finitely generated if submodule and quotient are finitely generated.
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
154530
Rings whose elements are partitioned between units and zero-divisors.
116526
Finite ring has only zero divisors and units
92583
Prove that $N(\gamma) = 1$ if, and only if, $\gamma$ is a unit in the ring $\mathbb{Z}[\sqrt{n}]$
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
116000
Prove that prime ideals of a finite ring are maximal
32795
Proving $ \bigcup_{i=1}^n A_{i} \text{ is finite.} $ by Induction.
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 $a,b \in R$.
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
73417
$Rad(I)$ is an ideal of $R$
86922
Ring with 10 elements is isomorphic to $\mathbb{Z}/10 \mathbb{Z} $
50809
Proving $R-S$ contains a prime ideal when $S$ is a multiplicative set
157605
$IS \mid JS$ implies that $I\mid J$ where $I$ and $J$ are ideals of a number ring contained in another number ring $S$