Theorems · Theorem · commutative algebra
RingHom.ker_isMaximal_of_surjective
∀ {R : Type u_1} {K : Type u_2} {F : Type u_3} [inst : Ring R] [inst_1 : DivisionRing K] [inst_2 : FunLike F R K]
[inst_3 : RingHomClass F R K] (f : F), Function.Surjective ⇑f → (RingHom.ker f).IsMaximalThe kernel of a homomorphism to a division ring is a maximal ideal.
- Defined in
- Mathlib.RingTheory.Ideal.Maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, 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.
- DFunLike.coestatement and proof · cited by 62,936
- Ringstatement and proof · cited by 7,463
- Bot.botproof · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- DivisionRingstatement and proof · cited by 1,062
- Ideal.IsMaximalstatement and proof · cited by 452
- RingHom.kerstatement · cited by 363
- RingHomClassstatement and proof · cited by 193
- Ideal.comap_isMaximal_of_surjectiveproof · cited by 8
- Ideal.bot_isMaximalproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 2
- IsLocalRing.ker_eq_maximalIdealproof · cited by 1
- Polynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 0