Definition:Local Ring/Noncommutative/Definition 4

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