Theorems · Theorem · commutative algebra
Ideal.map_mul
∀ {S : Type v} {F : Type u_1} [inst : CommSemiring S] {R : Type u_2} [inst_1 : Semiring R] [inst_2 : FunLike F R S]
[RingHomClass F R S] (f : F) (I J : Ideal R), Ideal.map f (I * J) = Ideal.map f I * Ideal.map f J- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 72 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
- Semiringstatement and proof · cited by 13,802
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- le_antisymmproof · cited by 2,068
- map_mulproof · cited by 1,137
- Ideal.mapstatement and proof · cited by 692
- RingHomClassstatement and proof · cited by 193
- Ideal.mem_map_of_memproof · cited by 71
Cited by9
Results whose statement or proof uses this declaration.
- Algebra.Generators.Cotangent.exactproof · cited by 6
- Ideal.IsDedekindDomain.ramificationIdx'_eq_one_iffproof · cited by 3
- Ideal.ramificationIdx'_eq_ramificationIdx'proof · cited by 3
- Ideal.ramificationIdx'_algebra_towerproof · cited by 2
- Ideal.IsDedekindDomain.emultiplicity_map_eq_ramificationIdx'_mulproof · cited by 2
- Algebra.Generators.sq_ker_comp_le_ker_compLocalizationAwayAlgHomproof · cited by 1
- Ideal.le_comap_mulproof · cited by 1
- Ideal.map_pointwise_smulproof · cited by 1
- Ideal.spanNorm_mulproof · cited by 0