Theorems · Theorem · commutative algebra
IsSMulRegular.of_isLocalizedModule
∀ {R : Type u_1} (S : Type u_2) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
(p : Submonoid R) [IsLocalization p S] {M : Type u_3} [inst_4 : AddCommMonoid M] [inst_5 : Module R M]
[inst_6 : Module S M] [IsScalarTower R S M] {K : Type u_6} [inst_8 : AddCommMonoid K] [inst_9 : Module R K]
(f : K →ₗ[R] M) [IsLocalizedModule p f] {x : R}, IsSMulRegular K x → IsSMulRegular M ((algebraMap R S) x)- Defined in
- Mathlib.RingTheory.Flat.Localization
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 106 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
Cited by1
Results whose statement or proof uses this declaration.
- IsSMulRegular.of_isLocalizationproof · cited by 0