Theorems · Theorem · commutative algebra
isSimpleRing_iff_isField
∀ (A : Type u_1) [inst : CommRing A], IsSimpleRing A ↔ IsField A
- Defined in
- Mathlib.RingTheory.SimpleRing.Field
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Subringproof · cited by 602
- RingEquiv.symmproof · cited by 567
- IsFieldstatement and proof · cited by 103
- IsSimpleRingstatement and proof · cited by 39
- RingEquiv.toMulEquivproof · cited by 26
- MulEquiv.isFieldproof · cited by 14
- Subring.topEquivproof · cited by 5
- IsSimpleRing.isField_centerproof · cited by 1
- Subring.center_eq_topproof · cited by 1
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