Theorems · Theorem · commutative algebra
ValuationSubring.mem_nonunits_iff
∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) {x : K}, x ∈ A.nonunits ↔ A.valuation x < 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- DFunLike.coestatement · cited by 62,936
- Fieldstatement and proof · cited by 7,404
- Valuationstatement · cited by 823
- ValuationSubringstatement and proof · cited by 187
- NonUnitalSubringstatement · cited by 185
- ValuationSubring.valuationstatement · cited by 29
- ValuationSubring.ValueGroupstatement · cited by 26
- ValuationSubring.nonunitsstatement · cited by 14
Cited by2
Results whose statement or proof uses this declaration.
- ValuationSubring.mem_nonunits_iff_orproof · cited by 1
- ValuationSubring.nonunits_leproof · cited by 1