Theorems · Theorem · commutative algebra
span_eq_top_of_isLocalizedModule
∀ {R : Type u_1} (Rₛ : Type u_2) [inst : CommSemiring R] (S : Submonoid R) [inst_1 : CommSemiring Rₛ]
[inst_2 : Algebra R Rₛ] [IsLocalization S Rₛ] {M : Type u_3} {Mₛ : Type u_4} [inst_4 : AddCommMonoid M]
[inst_5 : Module R M] [inst_6 : AddCommMonoid Mₛ] [inst_7 : Module R Mₛ] [inst_8 : Module Rₛ Mₛ]
[IsScalarTower R Rₛ Mₛ] (f : M →ₗ[R] Mₛ) [IsLocalizedModule S f] {v : Set M},
Submodule.span R v = ⊤ → Submodule.span Rₛ (⇑f '' v) = ⊤- Defined in
- Mathlib.RingTheory.Localization.Module
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites34
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- LinearMapstatement and proof · cited by 10,215
- Top.topstatement and proof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.imagestatement and proof · cited by 5,609
Cited by3
Results whose statement or proof uses this declaration.
- span_eq_top_localization_localizationproof · cited by 1
- KaehlerDifferential.span_range_map_derivation_of_isLocalizationproof · cited by 1
- Module.Finite.of_isLocalizedModuleproof · cited by 1