Theorems · Theorem · commutative algebra
Ideal.comap_isMaximal_of_surjective
∀ {R : Type u} {S : Type v} {F : Type u_1} [inst : Ring R] [inst_1 : Ring S] [inst_2 : FunLike F R S]
[inst_3 : RingHomClass F R S] (f : F),
Function.Surjective ⇑f → ∀ {K : Ideal S} [H : K.IsMaximal], (Ideal.comap f K).IsMaximal- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 8 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.
Cites25
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
- FunLikestatement and proof · cited by 2,560
- le_of_ltproof · cited by 1,175
- le_transproof · cited by 985
- Ideal.mapproof · cited by 692
- Ideal.IsMaximalstatement and proof · cited by 452
- Ideal.comapstatement and proof · cited by 443
- le_of_eqproof · cited by 366
- bot_leproof · cited by 306
Cited by8
Results whose statement or proof uses this declaration.
- Ideal.map_jacobson_of_surjectiveproof · cited by 4
- IsLocalHom.of_surjectiveproof · cited by 4
- RingHom.ker_isMaximal_of_surjectiveproof · cited by 3
- AdicCompletion.isMaximal_map_of_leproof · cited by 3
- Ideal.bot_quotient_isMaximal_iffproof · cited by 3
- Ideal.comap_jacobson_of_surjectiveproof · cited by 2
- Ideal.krullDimLE_zero_quotient_iff_forall_minimalPrimes_isMaximalproof · cited by 0
- PrimeSpectrum.comap_singleton_isClosed_of_surjectiveproof · cited by 0