Theorems · Definition · commutative algebra
Ideal.map
{R : Type u} →
{S : Type v} → {F : Type u_1} → [inst : Semiring R] → [inst_1 : Semiring S] → [FunLike F R S] → F → Ideal R → Ideal SI.map f is the span of the image of the ideal I under f, which may be bigger than
the image itself.
- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 692 results in Mathlib
- Foundations
- Depth 19 from the axioms, rests on 192 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- 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
- Ideal.spanproof · cited by 948
Cited by803
Results whose statement or proof uses this declaration.
- Ideal.ramificationIdx'proof · cited by 85
- Ideal.mem_map_of_memstatement · cited by 71
- Ideal.map_le_iff_le_comapstatement · cited by 60
- Ideal.ramificationIdxproof · cited by 59
- Ideal.map_spanstatement and proof · cited by 43
- Ideal.map_mapstatement · cited by 37
- Ideal.comap_map_of_surjectivestatement and proof · cited by 30
- HomogeneousIdeal.mapproof · cited by 30
- Ideal.map_monostatement · cited by 29
- Ideal.mem_map_iff_of_surjectivestatement and proof · cited by 19
- Ideal.spanNormproof · cited by 19
- Algebra.WeaklyQuasiFiniteAtproof · cited by 18
Showing the 200 most cited of 803.