Division Rings are also called skewfields.
Examples: Z is a commutative ring.
Mn(any ring), non-commutative and not every element has an inverse.
Q, R ,C are fields.
Example: Zn is a commutative ring. Zp is a field.
Def: Characteristic of a division ring.
Proposition 7.7: The characteristic of a division ring is either 0 or a prime.
Ex: Q,R,C have characteristic 0. Zp has characteristic p.
Def: The center of a division ring.
Proposition 7.11: The center of a division ring is a field.
Def: Automorphism of a division ring.
Ex: inner automorphism. Every automorphism of H is inner.
The skew Laurent series ring in one indeterminate.