Theorems · Definition · commutative algebra

LocalizedModule.lift

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      {M : Type u_2} →
        {M'' : Type u_4} →
          [inst_1 : AddCommMonoid M] →
            [inst_2 : AddCommMonoid M''] →
              [inst_3 : Module R M] →
                [inst_4 : Module R M''] →
                  (M →ₗ[R] M'') →
                    (∀ (x : ↥S), IsUnit ((algebraMap R (Module.End R M'')) ↑x)) → LocalizedModule S M →ₗ[R] M''

If g is a linear map M → M'' such that all scalar multiplication by s : S is invertible, then there is a linear map LocalizedModule S M → M''.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

14 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule