What are some examples of a non-commutative division ring other than quaternions?
2026-04-03 00:03:55.1775174635
On
Examples of a non-commutative division ring
4.1k Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
2
There are 2 best solutions below
0
On
Noncommutative domains which satisfy the right Ore condition allow you to build a "right division ring of fractions" in an analogous way to that of the field of fractions for a commutative domain.
This division ring is necessarily not commutative if you pick the domain to be not commutative :) Not commutative right Ore domains are pretty easy to come by: in particular, right Noetherian domains are right Ore. So for example, you could look at the division ring of quotients for $\Bbb H[x]$.
You can find many examples in:
R. S. Pierce, Associative algebras,Springer-Verlag, 1982