Theorems · Definition · commutative algebra

LocalizedModule.map

{R : Type u_1} →
  [inst : CommSemiring R] →
    (S : Submonoid R) →
      {M : Type u_2} →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Module R M] →
            {N : Type u_3} →
              [inst_3 : AddCommMonoid N] →
                [inst_4 : Module R N] → (M →ₗ[R] N) →ₗ[R] LocalizedModule S M →ₗ[Localization S] LocalizedModule S N

A linear map M →ₗ[R] N gives a map between localized modules Mₛ →ₗ[Rₛ] Nₛ.

Defined in

Mathlib.RingTheory.Localization.Module

Cited by

29 results in Mathlib

Foundations

Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringAddCommMonoidModuleAddCommMonoidModule