Theorems · Definition · commutative algebra

Algebra.Generators.baseChange

{R : Type u} →
  {S : Type v} →
    {ι : Type w} →
      [inst : CommRing R] →
        [inst_1 : CommRing S] →
          [inst_2 : Algebra R S] →
            (T : Type u_2) →
              [inst_3 : CommRing T] →
                [inst_4 : Algebra R T] → Algebra.Generators R S ι → Algebra.Generators T (TensorProduct R T S) ι

If P is a family of generators of S over R and T is an R-algebra, we obtain a natural family of generators of T ⊗[R] S over T.

Defined in

Mathlib.RingTheory.Extension.Generators

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommRingCommRingAlgebraCommRingAlgebra