Show that a finite domain is a division ring
14343
Every nonzero element in a finite ring is either a unit or a zero divisor
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?
111493
Division algorithm for polynomials in R[x], where R is a commutative ring with unity.
95408
Give an example to show that a factor ring of a ring with divisors of 0 may be an integral domain
116000
Prove that prime ideals of a finite ring are maximal
130466
Proving every prime ideal is maximal in a finite dimensional ring over a field.
93474
A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
112560
Simple Noetherian domain which is not a division ring
63568
Ring with finitely many zerodivisors
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
78350
When does a finite ring become a finite field?
95146
Polynomial ring $R[X] $ has zero Jacobson radical, for $R$ a domain
116651
Show for any simple ring without identity, R, that R is a division ring.
69728
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
154530
Rings whose elements are partitioned between units and zero-divisors.
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
50908
Showing a Ring and an Ideal are equal