Theorems · Definition · commutative algebra

Algebra.Generators.comp

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            {ι' : Type u_1} →
              {T : Type u_2} →
                [inst_3 : CommRing T] →
                  [inst_4 : Algebra R T] →
                    [inst_5 : Algebra S T] →
                      [IsScalarTower R S T] →
                        Algebra.Generators S T ι' → Algebra.Generators R S ι → Algebra.Generators R T (ι' ⊕ ι)

Given two families of generators S[X] → T and R[Y] → S, we may construct the family of generators R[X, Y] → T.

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

52 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower