Theorems · Theorem · commutative algebra
Ideal.map_pointwise_smul
∀ {R : Type u_4} {S : Type u_5} [inst : CommSemiring R] [inst_1 : CommSemiring S] (r : R) (I : Ideal R) (f : R →+* S),
Ideal.map f (r • I) = f r • Ideal.map f I- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- Submoduleproof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- Ideal.spanproof · cited by 948
- Ideal.mapstatement and proof · cited by 692
- smul_eq_mulproof · cited by 357
- Set.image_singletonproof · cited by 174
- Submodule.pointwiseDistribMulActionstatement · cited by 105
- Ideal.map_spanproof · cited by 43
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.Away.of_surjective_of_isScalarTowerproof · cited by 0