Definition:Residue Field of Local Ring
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Let $R$ be a commutative local ring.
Let $m$ be its maximal ideal.
The residue field is the quotient ring $R/m$.
- 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 ... (previous) ... (next) Chapter II: Localization: $\S3$ Local rings. Passage from the local to the global $1$: Local rings: Definition 1