Theorems · Theorem · commutative algebra

IsLocalizedModule.Away.mk

∀ {R : Type u_1} [inst : CommSemiring R] {M : Type u_2} {N : Type u_3} [inst_1 : AddCommMonoid M]
  [inst_2 : AddCommMonoid N] [inst_3 : Module R M] [inst_4 : Module R N] {f : M →ₗ[R] N} {r : R},
  IsUnit ((algebraMap R (Module.End R N)) r) →
    (∀ (x : N), ∃ n y, r ^ n • x = f y) →
      (∀ (x y : M), f x = f y → ∃ n, r ^ n • x = r ^ n • y) → IsLocalizedModule.Away r f

Defined in

Mathlib.Algebra.Module.LocalizedModule.Away

Cited by

2 results in Mathlib

Foundations

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

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule