Theorems · Definition · commutative algebra

Module.Basis.algebraMapCoeffs

{R : Type u_1} →
  (A : Type u_3) →
    {ι : Type u_5} →
      {M : Type u_6} →
        [inst : CommSemiring R] →
          [inst_1 : Semiring A] →
            [inst_2 : AddCommMonoid M] →
              [inst_3 : Algebra R A] →
                [inst_4 : Module A M] →
                  [inst_5 : Module R M] →
                    [IsScalarTower R A M] →
                      Module.Basis ι R M → Function.Bijective ⇑(algebraMap R A) → Module.Basis ι A M

If R and A have a bijective algebraMap R A and act identically on M, then a basis for M as R-module is also a basis for M as R'-module.

Defined in

Mathlib.RingTheory.AlgebraTower

Cited by

4 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAddCommMonoidAlgebraModuleModuleIsScalarTower