Definition:Local Ring/Noncommutative/Definition 4
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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 $R$.
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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