Is a left and right simple ring with unity a division ring?
135781
Division ring if and only if it has no proper left ideals.
1425
The Chinese Remainder Theorem for Rings.
76749
Example of a finite non-commutative ring without a unity
116651
Show for any simple ring without identity, R, that R is a division ring.
155120
Why are the only division algebras over the real numbers the real numbers, the complex numbers, and the quaternions?
15320
Morita equivalence and right and left ideals of a Ring
48009
Left inverse implies right inverse in a finite ring
138309
Ring whose all ideals are double-sided is commutative?
131319
I understand what a division ring is, but cannot find any examples. Can anyone give me one?
50908
Showing a Ring and an Ideal are equal
45575
why each left ideal of this is minimal?
63568
Ring with finitely many zerodivisors
108775
Identify the ring $\mathbb {Z}[i]/(2 + i) $
107900
A ring which has many distinct left inverses
133706
If R is a local ring, then its maximal left-ideal is a left and right ideal
62951
Is there a more direct way of proving that this ring is an integral domain?
60925
Why these are isomorphic each other for given these rings?