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Theorems · Theorem · commutative algebra

ValuationSubring.valuation_eq_iff

∀ {K : Type u} [inst : Field K] (A : ValuationSubring K) (x y : K), A.valuation x = A.valuation y ↔ ∃ a, ↑↑a * y = x
Defined in
Mathlib.RingTheory.Valuation.ValuationSubring
Cited by
1 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

ValuationSubring.valuation_unit · cited by 1ValuationSubring.valuatio…DFunLike.coe · cited by 62936DFunLike.coeField · cited by 7404FieldUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valValuation · cited by 823ValuationValuationSubring · cited by 187ValuationSubringQuotient.eq'' · cited by 44Quotient.eq''ValuationSubring.valuation · cited by 29ValuationSubring.valuationValuationSubring.ValueGroup · cited by 26ValuationSubring.ValueGro…ValuationSubring.valuation_eq…CITED BYCITES

Cites9

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Cited by1

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