Theorems · Theorem · commutative algebra
Ideal.map_span
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : FunLike F R S] (f : F)
[RingHomClass F R S] (s : Set R), Ideal.map f (Ideal.span s) = Ideal.span (⇑f '' s)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, 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.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Semiringstatement and proof · cited by 13,802
- Set.imagestatement and proof · cited by 5,609
- Idealstatement · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Submodule.spanproof · cited by 1,504
- Ideal.spanstatement and proof · cited by 948
- Ideal.mapstatement and proof · cited by 692
- Set.image_subset_iffproof · cited by 203
- RingHomClassstatement and proof · cited by 193
- Ideal.subset_spanproof · cited by 86
Cited by43
Results whose statement or proof uses this declaration.
- RingHom.OfLocalizationSpanTarget.ofLocalizationSpanproof · cited by 7
- Ideal.FG.mapproof · cited by 7
- Ideal.height_le_spanRank_toENat_of_mem_minimalPrimesproof · cited by 5
- Ideal.relNorm_algebraMapproof · cited by 4
- Ideal.lift_spanRank_map_leproof · cited by 3
- NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply_eq_spanproof · cited by 2
- AlgebraicGeometry.iSup_basicOpen_of_span_eq_topproof · cited by 2
- PowerSeries.eq_span_insert_X_of_X_mem_of_span_eqproof · cited by 2
- Ideal.isPrincipal_of_isPrincipal_isLocalizationAway_of_primeproof · cited by 2
- Ideal.height_le_height_add_spanFinrank_of_leproof · cited by 2
- Ideal.map_ofListproof · cited by 2
- Submodule.IsPrincipal.map_ringHomproof · cited by 2