Theorems · Theorem · ring theory
IsSimpleRing.isSemisimpleRing_iff_isArtinianRing
∀ {R : Type u} [inst : Ring R] [IsSimpleRing R], IsSemisimpleRing R ↔ IsArtinianRing R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingIsSimpleRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Idealproof · cited by 4,748
- List.TFAE.outproof · cited by 177
- IsAtomproof · cited by 130
- IsArtinianRingstatement and proof · cited by 98
- IsSimpleRingstatement and proof · cited by 39
- IsSemisimpleRingstatement and proof · cited by 28
- IsSimpleRing.tfaeproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- isSimpleRing_isArtinianRing_iffproof · cited by 1