Theorems · Inductive type · commutative algebra

IsLocalizedModule

{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'] → Submonoid R → (M →ₗ[R] M') → Prop

The characteristic predicate for localized module. IsLocalizedModule S f describes that f : M ⟶ M' is the localization map identifying M' as LocalizedModule S M.

Defined in

Mathlib.Algebra.Module.LocalizedModule.Basic

Cited by

220 results in Mathlib

Foundations

Depth 13 from the axioms, rests on 116 definitions · uses no axioms

Assumes

CommSemiringAddCommMonoidAddCommMonoidModuleModule