Theorems · Definition · commutative algebra

Algebra.Generators.ofComp

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            {ι' : Type u_3} →
              {T : Type u_7} →
                [inst_3 : CommRing T] →
                  [inst_4 : Algebra R T] →
                    [inst_5 : Algebra S T] →
                      [inst_6 : IsScalarTower R S T] →
                        (Q : Algebra.Generators S T ι') → (P : Algebra.Generators R S ι) → (Q.comp P).Hom Q

Given families of generators X ⊆ T over S and Y ⊆ S over R, there is a map of generators R[X, Y] → S[X].

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

32 results in Mathlib

Foundations

Depth 101 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower