Example of noncommutative ring in which all nonzero elements are invertible
131319
I understand what a division ring is, but cannot find any examples. Can anyone give me one?
9074
Example of non-isomorphic structures which are elementarily equivalent
8787
In a ring $(A,+, \cdot)$ if $aba = a$ then $bab = b$ and all non zero elements in $A$ are invertible.
32741
Idempotents in a ring without unity (rng) and no zero divisors.
107378
If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses.
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
120496
Examples of Non-Noetherian Valuation Rings
69160
Show that the functor that takes $R$ to the set of invertible elements of $R[X]/(X^2-a)$ is representable.
34798
Example of element of double dual that is not an evaluation map
48009
Left inverse implies right inverse in a finite ring
30465
Determining which rings have a module which is not semisimple
134991
Commutative non Noetherian rings in which all maximal ideals are finitely generated
112131
Characterizing all ring homomorphisms $C[0,1]\to\mathbb{R}$.
94203
Examples for almost-semirings without absorbing zero
46303
Example of a non-Noetherian complete local ring
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?