Theorems · Theorem · commutative algebra

Module.Basis.smulTower_repr

∀ {R : Type u_1} {S : Type u_2} {A : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid A]
  [inst_3 : Module R S] [inst_4 : Module S A] [inst_5 : Module R A] [inst_6 : IsScalarTower R S A] {ι : Type u_5}
  {ι' : Type u_6} (b : Module.Basis ι R S) (c : Module.Basis ι' S A) (x : A) (ij : ι × ι'),
  ((b.smulTower c).repr x) ij = (b.repr ((c.repr x) ij.2)) ij.1

Defined in

Mathlib.RingTheory.AlgebraTower

Cited by

4 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleModuleModuleIsScalarTower