Theorems · Theorem · ring theory
TwoSidedIdeal.ker_eq_bot
∀ {R : Type u_1} {S : Type u_2} [inst : NonUnitalNonAssocRing R] [inst_1 : NonUnitalNonAssocSemiring S] {F : Type u_3}
[inst_2 : FunLike F R S] [inst_3 : NonUnitalRingHomClass F R S] (f : F),
TwoSidedIdeal.ker f = ⊥ ↔ Function.Injective ⇑f- Defined in
- Mathlib.RingTheory.TwoSidedIdeal.Kernel
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 51 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.
- DFunLike.coestatement and proof · cited by 62,936
- Bot.botstatement and proof · cited by 4,720
- FunLikestatement and proof · cited by 2,560
- NonUnitalNonAssocSemiringstatement and proof · cited by 1,081
- NonUnitalNonAssocRingstatement and proof · cited by 354
- eq_bot_iffproof · cited by 159
- TwoSidedIdealstatement · cited by 151
- NonUnitalRingHomClassstatement and proof · cited by 82
- TwoSidedIdeal.ringConproof · cited by 40
- TwoSidedIdeal.kerstatement and proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- IsSimpleRing.injective_ringHom_or_subsingleton_codomainproof · cited by 2
- IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomainproof · cited by 1