Theorems · Theorem · ring theory
isSimpleRing_iff_isTwoSided_imp
∀ {R : Type u_1} [inst : Ring R], IsSimpleRing R ↔ Nontrivial R ∧ ∀ (I : Ideal R), I.IsTwoSided → I = ⊥ ∨ I = ⊤- Defined in
- Mathlib.RingTheory.SimpleRing.Congr
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Idealstatement and proof · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- Equiv.symmproof · cited by 3,681
- Nontrivialstatement and proof · cited by 2,416
- OrderIsoproof · cited by 874
- NonUnitalNonAssocRingproof · cited by 354
- Ideal.IsTwoSidedstatement and proof · cited by 179
- TwoSidedIdealproof · cited by 151
- RelIso.toEquivproof · cited by 113
Cited by1
Results whose statement or proof uses this declaration.
- IsSimpleRing.tfaeproof · cited by 1