Definition:Local Ring/Noncommutative/Definition 2
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Let $R$ be a ring with unity.
$R$ is a local ring if and only if it has a unique maximal right ideal.
- 1991: T.Y. Lam: A First Course in Noncommutative Rings ... (previous) ... (next): Chapter $7$: Local Rings, Semilocal Rings, and Idempotents: $\S19$: Local Rings: Theorem 19.1