Theorems · Theorem · commutative algebra
isLocalizedModule_iff_isLocalization
∀ {R : Type u_1} [inst : CommSemiring R] {S : Submonoid R} {A : Type u_2} {Aₛ : Type u_3} [inst_1 : CommSemiring A]
[inst_2 : Algebra R A] [inst_3 : CommSemiring Aₛ] [inst_4 : Algebra A Aₛ] [inst_5 : Algebra R Aₛ]
[inst_6 : IsScalarTower R A Aₛ],
IsLocalizedModule S (IsScalarTower.toAlgHom R A Aₛ).toLinearMap ↔ IsLocalization (Algebra.algebraMapSubmonoid A S) Aₛ- Cited by
- 4 results in Mathlib
- Foundations
- Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Algebra.algebraMapproof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- mul_commproof · cited by 2,262
- IsUnitproof · cited by 1,602
- Module.Endproof · cited by 774
- IsLocalizationstatement and proof · cited by 636
- Algebra.smul_defproof · cited by 287
Cited by4
Results whose statement or proof uses this declaration.
- Algebra.isLocalization_iff_isPushoutproof · cited by 4
- Polynomial.isLocalizationproof · cited by 2
- isLocalizedModule_iff_isLocalization'proof · cited by 1
- TensorProduct.toIntegralClosure_bijective_of_isLocalizationAwayproof · cited by 1