Theorems · Theorem · commutative algebra
Ideal.comap_eq_top_iff
∀ {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}
[inst_3 : RingHomClass F R S] {I : Ideal S}, Ideal.comap f I = ⊤ ↔ I = ⊤- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.eq_top_iff_oneproof · cited by 56
- Ideal.mem_comapproof · cited by 54
- Ideal.comap_topproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.isMaximal_of_isIntegral_of_isMaximal_comapproof · cited by 5
- RingOfIntegers.exponent_eq_one_iffproof · cited by 2
- Ideal.eq_top_iff_of_liesOverproof · cited by 2
- IsLocalization.AtPrime.radical_map_of_mem_minimalPrimesproof · cited by 1
- isJacobsonRing_of_isIntegralproof · cited by 1