Theorems · Definition · commutative algebra
Ideal.comap
{R : Type u} →
{S : Type v} →
{F : Type u_1} →
[inst : Semiring R] →
[inst_1 : Semiring S] → [inst_2 : FunLike F R S] → F → [RingHomClass F R S] → Ideal S → Ideal RI.comap f is the preimage of I under f.
- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 443 results in Mathlib
- Foundations
- Depth 17 from the axioms, rests on 194 definitions · uses propext
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.preimageproof · cited by 4,946
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- RingHomClassstatement and proof · cited by 193
Cited by489
Results whose statement or proof uses this declaration.
- RingHom.kerproof · cited by 363
- PrimeSpectrum.comapproof · cited by 199
- Ideal.underproof · cited by 170
- Ideal.map_le_iff_le_comapstatement · cited by 60
- Localization.localRingHomstatement and proof · cited by 54
- Ideal.mem_comapstatement · cited by 54
- Ideal.inertiaDeg'proof · cited by 33
- Ideal.comap_map_of_surjectivestatement and proof · cited by 30
- Ideal.comap.congr_simpstatement and proof · cited by 29
- Ideal.prodproof · cited by 28
- Ideal.comap_comapstatement · cited by 27
- Ideal.quotientMapstatement and proof · cited by 27
Showing the 200 most cited of 489.