Definition:Division Ring/Definition 2

Definition

A division ring is a ring with unity $\struct {R, +, \circ}$ such that:

Every non-zero element of $R$ is a unit.

Also see

• Equivalence of Definitions of Division Ring

• Results about division rings can be found here.

Sources

• 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 6$: Rings and fields