Theorems · Theorem · commutative algebra
IsLocalRing.ResidueField.mapAlgHom_residue
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : IsLocalRing S]
[inst_3 : CommRing T] [inst_4 : IsLocalRing T] [inst_5 : Algebra R S] [inst_6 : Algebra R T] (e : S →ₐ[R] T)
[inst_7 : IsLocalHom e] (x : S),
(IsLocalRing.ResidueField.mapAlgHom e) ((IsLocalRing.residue S) x) = (IsLocalRing.residue T) (e x)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- AlgHomstatement and proof · cited by 3,236
- IsLocalRingstatement and proof · cited by 339
- IsLocalRing.ResidueFieldstatement · cited by 156
- IsLocalHomstatement and proof · cited by 100
- IsLocalRing.residuestatement · cited by 71
- IsLocalRing.ResidueField.mapAlgHomstatement · cited by 1
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