Definition:Local Ring/Noncommutative/Definition 3
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Definition
Let $R$ be a ring with unity.
Let $\operatorname {rad} R$ be its Jacobson radical.
Then $R$ is a local ring if and only if the quotient ring $R / \operatorname {rad} R$ is a division ring.
Sources
- 1991: T.Y. Lam: A First Course in Noncommutative Rings ... (previous): Chapter $7$: Local Rings, Semilocal Rings, and Idempotents: $\S19$: Local Rings: Theorem $19.1$