Theorems · Theorem · commutative algebra

IsLocalizedModule.eq_iff_exists

∀ {R : Type u_1} [inst : CommSemiring R] (S : Submonoid 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'] (f : M →ₗ[R] M') [IsLocalizedModule S f]
  {x₁ x₂ : M}, f x₁ = f x₂ ↔ ∃ c, c • x₁ = c • x₂

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

8 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModuleIsLocalizedModule