Theorems · Theorem · commutative algebra
Ideal.smul_restrictScalars
∀ {R : Type u_4} {S : Type u_5} {M : Type u_6} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S]
[inst_3 : AddCommMonoid M] [inst_4 : Module R M] [inst_5 : Module S M] [inst_6 : IsScalarTower R S M] (I : Ideal R)
(N : Submodule S M),
Submodule.restrictScalars R (Ideal.map (algebraMap R S) I • N) = I • Submodule.restrictScalars R N- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 3 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.
Cites23
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 by3
Results whose statement or proof uses this declaration.
- Ideal.smul_top_eq_mapproof · cited by 15
- Algebra.FormallySmooth.of_surjective_of_ker_eq_map_of_flatproof · cited by 1
- RingTheory.Sequence.isRegular_cons_iff'proof · cited by 1