Theorems · Theorem · commutative algebra
Ideal.comap_ne_top
∀ {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)
{K : Ideal S} [inst_3 : RingHomClass F R S], K ≠ ⊤ → Ideal.comap f K ≠ ⊤- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement and proof · cited by 13,802
- Top.topstatement and proof · cited by 9,680
- Idealstatement and proof · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- map_oneproof · cited by 861
- Ideal.comapstatement and proof · cited by 443
- RingHomClassstatement and proof · cited by 193
- Ideal.mem_comapproof · cited by 54
- Ideal.ne_top_iff_oneproof · cited by 16
Cited by7
Results whose statement or proof uses this declaration.
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- Ideal.comap_map_eq_self_of_isMaximalproof · cited by 2
- Ideal.mem_primesOver_iff_mem_normalizedFactorsproof · cited by 2
- Ideal.liesOver_span_iffproof · cited by 1
- Ideal.under_map_eq_map_underproof · cited by 1
- Ideal.liesOver_iff_dvd_mapproof · cited by 1
- Ideal.IsPrimary.comapproof · cited by 0