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Theorems · Theorem · commutative algebra

ValuativeRel.eq_trivialRel_of_compatible_one

∀ {R Γ : Type} [inst : Ring R] [inst_1 : DecidableEq R] [inst_2 : IsDomain R]
  [inst_3 : LinearOrderedCommGroupWithZero Γ] [h : ValuativeRel R] [hv : Valuation.Compatible 1],
  h = ValuativeRel.trivialRel
Defined in
Mathlib.RingTheory.Valuation.ValuativeRel.Trivial
Cited by
1 results in Mathlib
Foundations
Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingDecidableEqIsDomainLinearOrderedCommGroupWithZeroValuativeRelValuation.Compatible
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

ValuativeRel.trivialRel_eq_ofValuation_one · cited by 0ValuativeRel.trivialRel_e…DFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingIsDomain · cited by 2196IsDomainmap_zero · cited by 1614map_zeroValuation · cited by 823ValuationLinearOrderedCommGroupWithZero · cited by 528LinearOrderedCommGroupWit…ValuativeRel · cited by 241ValuativeRelValuation.Compatible · cited by 71Valuation.CompatibleValuation.one_apply_of_ne_zero · cited by 3Valuation.one_apply_of_ne…Valuation.Compatible.vle_iff_le · cited by 3Compatible.vle_iff_leValuativeRel.ext · cited by 2ValuativeRel.extValuativeRel.trivialRel · cited by 2ValuativeRel.trivialRelValuativeRel.eq_trivialRel_of…CITED BYCITES

Cites12

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Cited by1

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