Definition:Local Ring/Commutative/Definition 1
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Definition
Let $A$ be a commutative ring with unity.
The ring $A$ is local if and only if it has a unique maximal ideal.
Also see
Sources
- 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra: Chapter $1$: Rings and Ideals: $\S$ Prime Ideals and Maximal Ideals
- 1972: N. Bourbaki: Commutative Algebra ... (next) Chapter $\text {II}$: Localization: $\S 3$ Local rings. Passage from the local to the global $1$: Local rings: Definition $1$