Theorems · Theorem · commutative algebra
Submodule.restrictScalars_map_smul_eq
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_3} {M : Type u_4} [inst_1 : CommSemiring S] [inst_2 : Algebra S R]
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower S R M] (I : Ideal S)
(N : Submodule R M),
Submodule.restrictScalars S (Ideal.map (algebraMap S R) I • N) = I • Submodule.restrictScalars S N- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommMonoidstatement and proof · cited by 12,281
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Submodulestatement and proof · cited by 7,192
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerstatement and proof · cited by 3,896
Cited by2
Results whose statement or proof uses this declaration.
- IsHausdorff.map_algebraMap_iffproof · cited by 1
- IsPrecomplete.map_algebraMap_iffproof · cited by 0