# Definition:Division Ring/Definition 3

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## Definition

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

- $R$ has no proper elements.

## Also see

- Results about
**division rings**can be found here.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 23$ - 1972: A.G. Howson:
*A Handbook of Terms used in Algebra and Analysis*... (previous) ... (next): $\S 6$: Rings and fields - 1978: Thomas A. Whitelaw:
*An Introduction to Abstract Algebra*... (previous) ... (next): $\S 55 \ (3)$. The definition of a ring and its elementary consequences