# Definition:Local Ring/Noncommutative/Definition 4

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## Definition

Let $R$ be a ring with unity.

$R$ is a **local ring** if and only if:

- $R$ is nontrivial
- the sum of any two non-units of $R$ is a non-unit of $R$.

## Sources

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- 1991: T.Y. Lam:
*A First Course in Noncommutative Rings*: Chapter $7$: Local Rings, Semilocal Rings, and Idempotents: $\S 19$: Local Rings