Theorems · Definition · commutative algebra

IsBaseChange.basis

{R : Type u_1} →
  [inst : CommSemiring R] →
    {S : Type u_2} →
      [inst_1 : CommSemiring S] →
        [inst_2 : Algebra R S] →
          {V : Type u_3} →
            [inst_3 : AddCommMonoid V] →
              [inst_4 : Module R V] →
                {W : Type u_4} →
                  [inst_5 : AddCommMonoid W] →
                    [inst_6 : Module R W] →
                      [inst_7 : Module S W] →
                        [inst_8 : IsScalarTower R S W] →
                          {ι : Type u_5} → {ε : V →ₗ[R] W} → Module.Basis ι R V → IsBaseChange S ε → Module.Basis ι S W

The basis of a module deduced by base change from a free module with a basis.

Defined in

Mathlib.RingTheory.TensorProduct.IsBaseChangeFree

Cited by

8 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringAlgebraAddCommMonoidModuleAddCommMonoidModuleModuleIsScalarTower