Theorems · Theorem · ring theory
IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomain
∀ (R : Type u) [inst : NonAssocRing R] [Nontrivial R],
IsSimpleRing R ↔ ∀ {S : Type u} [inst_2 : NonAssocSemiring S] (f : R →+* S), Function.Injective ⇑f ∨ Subsingleton S- Defined in
- Mathlib.RingTheory.SimpleRing.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- RingHomstatement and proof · cited by 10,189
- Top.topproof · cited by 9,680
- Nontrivialstatement and proof · cited by 2,416
- le_antisymmproof · cited by 2,068
- NonAssocSemiringstatement and proof · cited by 805
- NonAssocRingstatement and proof · cited by 483
- le_topproof · cited by 411
- bot_leproof · cited by 306
- TwoSidedIdealproof · cited by 151
- RingCon.Quotientproof · cited by 118
- RingCon.toQuotientproof · cited by 69
Cited by1
Results whose statement or proof uses this declaration.
- IsSimpleRing.iff_injective_ringHomproof · cited by 0