Theorems · Theorem · commutative algebra

IsLocalizedModule.exists_of_eq

∀ {R : Type u_1} {inst : CommSemiring R} {M : Type u_2} {M' : Type u_3} {inst_1 : AddCommMonoid M}
  {inst_2 : AddCommMonoid M'} {inst_3 : Module R M} {inst_4 : Module R M'} {S : Submonoid R} {f : M →ₗ[R] M'}
  [self : IsLocalizedModule S f] {x₁ x₂ : M}, f x₁ = f x₂ → ∃ c, c • x₁ = c • x₂

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

10 results in Mathlib

Foundations

Depth 21 from the axioms · uses no axioms

Assumes

IsLocalizedModule