Theorems · Theorem · commutative algebra
Ideal.comap_injective_of_surjective
∀ {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], Function.Surjective ⇑f → Function.Injective (Ideal.comap f)- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- Idealstatement · cited by 4,748
- FunLikestatement and proof · cited by 2,560
- Ideal.comapstatement · cited by 443
- RingHomClassstatement and proof · cited by 193
- GaloisInsertion.u_injectiveproof · cited by 10
- Ideal.giMapComapproof · cited by 6
Cited by8
Results whose statement or proof uses this declaration.
- Ideal.map_eq_top_or_isMaximal_of_surjectiveproof · cited by 6
- PrimeSpectrum.comap_injective_of_surjectiveproof · cited by 5
- ringKrullDim_le_of_surjectiveproof · cited by 4
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Ideal.ncard_primesOver_lt_of_not_leproof · cited by 1
- Ideal.map_eq_iff_sup_ker_eq_of_surjectiveproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_restrictScalarsproof · cited by 1
- Ideal.minimalPrimes_map_of_surjectiveproof · cited by 0