Theorems · Theorem · commutative algebra
Submodule.restrictScalars_image_smul_eq
∀ {R : Type u} [inst : CommSemiring R] {S : Type u_1} {M : Type u_2} [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] (s : Set S)
(N : Submodule R M), Submodule.restrictScalars S (⇑(algebraMap S R) '' s • N) = s • Submodule.restrictScalars S N- Defined in
- Mathlib.Algebra.Algebra.Operations
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites33
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
- 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.imagestatement and proof · cited by 5,609
- Finsuppproof · cited by 5,255
- Algebra.algebraMapstatement and proof · cited by 4,706
Cited by2
Results whose statement or proof uses this declaration.
- AdicCompletion.pow_smul_top_eq_ker_evalproof · cited by 4
- Submodule.restrictScalars_map_smul_eqproof · cited by 2