Theorems · Theorem · ring theory
IsSimpleRing.iff_injective_ringHom
∀ (R : Type u) [inst : NonAssocRing R] [Nontrivial R],
IsSimpleRing R ↔ ∀ {S : Type u} [inst_2 : NonAssocSemiring S] [Nontrivial S] (f : R →+* S), Function.Injective ⇑f- Defined in
- Mathlib.RingTheory.SimpleRing.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 54 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingNontrivial
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Cites8
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
- Nontrivialstatement and proof · cited by 2,416
- NonAssocSemiringstatement and proof · cited by 805
- NonAssocRingstatement and proof · cited by 483
- subsingleton_or_nontrivialproof · cited by 161
- IsSimpleRingstatement · cited by 39
- IsSimpleRing.iff_injective_ringHom_or_subsingleton_codomainproof · cited by 1
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