Theorems · Definition · linear algebra

Module.Basis.baseChange

{R : Type u_1} →
  {M : Type u_3} →
    {ι : Type u_5} →
      [inst : CommSemiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            (S : Type u_7) →
              [inst_3 : Semiring S] →
                [inst_4 : Algebra R S] → Module.Basis ι R M → Module.Basis ι S (TensorProduct R S M)

The lift of an R-basis of M to an S-basis of the base change S ⊗[R] M.

Defined in

Mathlib.LinearAlgebra.TensorProduct.Basis

Cited by

9 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleSemiringAlgebra