Theorems · Theorem · commutative algebra
RingHom.EssFiniteType.residueFieldMap
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] {f : R →+* S} [inst_2 : IsLocalRing R]
[inst_3 : IsLocalRing S] [inst_4 : IsLocalHom f], f.EssFiniteType → (IsLocalRing.ResidueField.map f).EssFiniteType- Defined in
- Mathlib.RingTheory.RingHom.EssFiniteType
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- RingHomstatement and proof · cited by 10,189
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.ResidueFieldstatement and proof · cited by 156
- IsLocalHomstatement and proof · cited by 100
- IsLocalRing.residueproof · cited by 71
- IsLocalRing.ResidueField.mapstatement · cited by 16
- RingHom.EssFiniteTypestatement and proof · cited by 14
- IsLocalRing.residue_surjectiveproof · cited by 11
- RingHom.FiniteType.essFiniteTypeproof · cited by 4
- RingHom.FiniteType.of_surjectiveproof · cited by 3
- RingHom.EssFiniteType.compproof · cited by 2
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