Theorems · Theorem · commutative algebra
Ideal.map_isPrime_of_surjective
∀ {R : Type u_1} {S : Type u_2} {F : Type u_3} [inst : Ring R] [inst_1 : Ring S] [inst_2 : FunLike F R S]
[rc : RingHomClass F R S] {f : F},
Function.Surjective ⇑f → ∀ {I : Ideal R} [H : I.IsPrime], RingHom.ker f ≤ I → (Ideal.map f I).IsPrime- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- Top.topproof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- map_mulproof · cited by 1,137
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.mapstatement and proof · cited by 692
- map_subproof · cited by 565
- Ideal.comapproof · cited by 443
- sub_eq_zeroproof · cited by 407
Cited by11
Results whose statement or proof uses this declaration.
- Ideal.isPrime_map_quotientMk_of_isPrimeproof · cited by 4
- Ideal.minimalPrimes_comap_of_surjectiveproof · cited by 3
- PrimeSpectrum.exists_comap_evalRingHom_eqproof · cited by 3
- Algebra.WeaklyQuasiFiniteAt.baseChangeproof · cited by 2
- Ideal.mem_minimalPrimes_span_of_mem_minimalPrimes_span_insertproof · cited by 1
- Polynomial.isJacobsonRing_polynomial_of_isJacobsonRingproof · cited by 1
- Ideal.map_height_le_one_of_mem_minimalPrimesproof · cited by 1
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1
- image_comap_zeroLocus_eq_zeroLocus_comapproof · cited by 1
- Ideal.map_radical_of_surjectiveproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.eq_of_le_of_under_eqproof · cited by 0