Theorems · Theorem · commutative algebra

LinearEquiv.restrictScalars_apply

∀ (R : Type u_1) {S : Type u_4} {M : Type u_5} {M₂ : Type u_7} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] [inst_4 : Module R M] [inst_5 : Module R M₂]
  [inst_6 : Module S M] [inst_7 : Module S M₂] [inst_8 : LinearMap.CompatibleSMul M M₂ R S] (f : M ≃ₗ[S] M₂) (a : M),
  (LinearEquiv.restrictScalars R f) a = f a

Defined in

Mathlib.Algebra.Module.Equiv.Basic

Cited by

16 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidModuleModuleModuleModuleLinearMap.CompatibleSMul