Theorems · Definition · commutative algebra

IsLocalRing.ResidueField.mapAlgHom

{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) → [IsLocalHom e] → IsLocalRing.ResidueField S →ₐ[R] IsLocalRing.ResidueField T

A local algebra homomorphism induces an algebra homomorphism on the residue fields. See mapAlgHom' for a variant where the base ring R is also quotiented.

Defined in

Mathlib.RingTheory.LocalRing.ResidueField.Basic

Cited by

1 results in Mathlib

Foundations

Depth 100 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingIsLocalRingCommRingIsLocalRingAlgebraAlgebraIsLocalHom