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Theorems · Definition · commutative algebra

Valuation.RankOne.ofRankLeOneStruct

{R : Type u_3} →
  [inst : Ring R] →
    [inst_1 : ValuativeRel R] →
      [ValuativeRel.IsNontrivial R] → ValuativeRel.RankLeOneStruct R → (ValuativeRel.valuation R).RankOne

A valuative relation has a rank one valuation when it is both nontrivial and the rank is at most one.

Defined in
Mathlib.RingTheory.Valuation.RankOne
Cited by
0 results in Mathlib
Foundations
Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingValuativeRelValuativeRel.IsNontrivial
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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Ring · cited by 7463RingValuativeRel · cited by 241ValuativeRelValuativeRel.ValueGroupWithZero · cited by 86ValuativeRel.ValueGroupWi…ValuativeRel.valuation · cited by 42ValuativeRel.valuationValuation.RankOne · cited by 32Valuation.RankOneValuativeRel.IsNontrivial · cited by 12ValuativeRel.IsNontrivialValuativeRel.RankLeOneStruct · cited by 7ValuativeRel.RankLeOneStr…RankOne.ofRankLeOneStructCITED BYCITES

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