Theorems · Theorem · ring theory
IsSimpleRing.one_mem_of_ne_zero_mem
∀ {A : Type u_2} [inst : NonAssocRing A] [IsSimpleRing A] (I : TwoSidedIdeal A) {x : A}, x ≠ 0 → x ∈ I → 1 ∈ I- Defined in
- Mathlib.RingTheory.SimpleRing.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 53 from the axioms · uses propext, Quot.sound
- Assumes
- NonAssocRingIsSimpleRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Bot.botproof · cited by 4,720
- NonAssocRingstatement and proof · cited by 483
- TwoSidedIdealstatement and proof · cited by 151
- IsSimpleRingstatement and proof · cited by 39
- IsSimpleRing.one_mem_of_ne_botproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- IsSimpleRing.isField_centerproof · cited by 1