Theorems · Theorem · commutative algebra
IsSimpleRing.isField_center
∀ (A : Type u_1) [inst : Ring A] [IsSimpleRing A], IsField ↥(Subring.center A)
- Defined in
- Mathlib.RingTheory.SimpleRing.Field
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 54 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.
Cites18
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
- Set.rangeproof · cited by 4,705
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- mul_assocproof · cited by 1,667
- Subringstatement · cited by 602
- mul_negproof · cited by 590
- mul_addproof · cited by 413
- TwoSidedIdealproof · cited by 151
- IsFieldstatement · cited by 103
Cited by1
Results whose statement or proof uses this declaration.
- isSimpleRing_iff_isFieldproof · cited by 0