Theorems · Definition · field theory
Field.ofIsUnitOrEqZero
{R : Type u_3} → [Nontrivial R] → [inst : CommRing R] → (∀ (a : R), IsUnit a ∨ a = 0) → Field RConstructs a Field structure on a CommRing consisting only of units and 0.
- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NontrivialCommRing
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.
- CommRingstatement and proof · cited by 17,173
- Fieldstatement · cited by 7,404
- Nontrivialstatement and proof · cited by 2,416
- IsUnitstatement and proof · cited by 1,602
- DivisionRingproof · cited by 1,062
- DivisionRing.mul_inv_cancelproof · cited by 1
- DivisionRing.nnqsmulproof · cited by 1
- DivisionRing.qsmulproof · cited by 1
- DivisionRing.qsmul_defproof · cited by 1
- DivisionRing.ratCast_defproof · cited by 1
- DivisionRing.div_eq_mul_invproof · cited by 0
- DivisionRing.inv_zeroproof · cited by 0
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