Are all the division rings simple?
114688
Show that a division ring is simple.
112560
Simple Noetherian domain which is not a division ring
57732
Rings of fractions and homomorphisms
52966
Rings, ideals and units-proof
107900
A ring which has many distinct left inverses
127306
Is the group of units of a finite ring cyclic?
34203
if $S$ is a ring (possibly without identity) with no proper left ideals, then either $S^2=0$ or $S$ is a division ring.
6646
A (non-artificial) example of a ring without maximal ideals
11541
Examples of a non-commutative division ring
67342
Why does a minimal prime ideal consist of zerodivisors?
146276
Is there a ring such that the nilradical of it is not nilpotent?
19310
Identify the ring $\mathbb{Z}[x]/(2x)$
1141
Existence of totally ordered ring with zero divisors
46047
Check whether the quotient ring $R:=\mathbb{C}[x,y,z]/(xy-z^2)$ is a field or an integral domain
133738
Can a ring without a unit element have a subring with a unit element?
116526
Finite ring has only zero divisors and units
154530
Rings whose elements are partitioned between units and zero-divisors.