Definition:Residue Field of Local Ring

Definition

Let $R$ be a commutative local ring.

Let $m$ be its maximal ideal.

The residue field of $R$ is the quotient ring $R / m$.

Also see

• Maximal Ideal iff Quotient Ring is Field

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 ... (previous) ... (next) Chapter II: Localization: $\S3$ Local rings. Passage from the local to the global $1$: Local rings: Definition 1