Theorems · Theorem · commutative algebra

LinearEquiv.toLinearMap_inj

∀ {R : Type u_1} {S : Type u_6} {M : Type u_7} {M₂ : Type u_9} [inst : Semiring R] [inst_1 : Semiring S]
  [inst_2 : AddCommMonoid M] [inst_3 : AddCommMonoid M₂] {modM : Module R M} {modM₂ : Module S M₂} {σ : R →+* S}
  {σ' : S →+* R} [inst_4 : RingHomInvPair σ σ'] [inst_5 : RingHomInvPair σ' σ] {e₁ e₂ : M ≃ₛₗ[σ] M₂},
  ↑e₁ = ↑e₂ ↔ e₁ = e₂

Defined in

Mathlib.Algebra.Module.Equiv.Defs

Cited by

14 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidAddCommMonoidRingHomInvPairRingHomInvPair