Definition:Local Ring/Noncommutative/Definition 1

Definition

Let $R$ be a ring with unity.

$R$ is a local ring if and only if it has a unique maximal left ideal.

Sources

• 1991: T.Y. Lam: A First Course in Noncommutative Rings ... (next): Chapter $7$: Local Rings, Semilocal Rings, and Idempotents: $\S19$: Local Rings: Theorem $19.1$