Definition:Division Ring

Definition
A division ring is a ring with unity $\struct {R, +, \circ}$ with one of the following equivalent properties:

Also known as
Some sources use this as the definition of a field, although this is non-standard: it is usually specified that a field product has to be commutative.

Also see

 * Equivalence of Definitions of Division Ring


 * Definition:Field (Abstract Algebra)
 * Definition:Skew Field