Theorems · Definition · commutative algebra
IsLocalRing.ResidueField
(R : Type u_1) → [inst : CommRing R] → [IsLocalRing R] → Type u_1
The residue field of a local ring is the quotient of the ring by its maximal ideal.
- Cited by
- 156 results in Mathlib
- Foundations
- Depth 71 from the axioms, rests on 1,039 definitions · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- HasQuotient.Quotientproof · cited by 2,301
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.maximalIdealproof · cited by 297
Cited by190
Results whose statement or proof uses this declaration.
- Ideal.ResidueFieldproof · cited by 119
- AlgebraicGeometry.Scheme.residueFieldproof · cited by 95
- IsLocalRing.residuestatement · cited by 71
- ArchimedeanClass.FiniteResidueField.mkproof · cited by 22
- ArchimedeanClass.FiniteResidueFieldproof · cited by 17
- IsLocalRing.ResidueField.mapstatement · cited by 16
- AlgebraicGeometry.LocallyRingedSpace.residueFieldproof · cited by 16
- PowerSeries.IsWeierstrassDivisor.of_map_ne_zerostatement and proof · cited by 11
- IsLocalRing.residue_surjectivestatement · cited by 11
- PowerSeries.weierstrassDistinguishedstatement · cited by 8
- PowerSeries.weierstrassUnitstatement · cited by 8
- Module.free_of_flat_of_isLocalRingproof · cited by 7