Definition:Skew Field
Jump to navigation
Jump to search
Definition
A skew field is a division ring whose ring product is specifically not commutative.
Also known as
The term sfield is sometimes encountered.
Some sources do not bother to give a specific name to this concept, but merely refer to a non-commutative division ring.
Examples
Quaternions form Skew Field
The set $\H$ of quaternions forms a skew field under the operations of addition and multiplication.
Also see
- Results about skew fields can be found here.
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {IV}$: Rings and Fields: $23$. The Field of Rational Numbers