Theorems · Definition · commutative algebra

Algebra.Extension.Hom.mapKer

{R : Type u} →
  {S : Type v} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          {P : Algebra.Extension R S} →
            {R' : Type u_1} →
              {S' : Type u_2} →
                [inst_3 : CommRing R'] →
                  [inst_4 : CommRing S'] →
                    [inst_5 : Algebra R' S'] →
                      {P' : Algebra.Extension R' S'} →
                        [inst_6 : Algebra R R'] →
                          [inst_7 : Algebra S S'] →
                            (f : P.Hom P') →
                              [alg : Algebra P.Ring P'.Ring] →
                                algebraMap P.Ring P'.Ring = f.toRingHom → ↥P.ker →ₗ[P.Ring] ↥P'.ker

A map between extensions induce a map between kernels.

Defined in

Mathlib.RingTheory.Extension.Basic

Cited by

5 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingCommRingAlgebraAlgebraAlgebraAlgebra