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Theorems · Theorem · commutative algebra

Valuation.RankOne.nontrivial

∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
  [hv : v.RankOne], ∃ r, v r ≠ 0 ∧ v r ≠ 1
Defined in
Mathlib.RingTheory.Valuation.RankOne
Cited by
1 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingLinearOrderedCommGroupWithZeroValuation.RankOne
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Valuation.RankOne.unit · cited by 1RankOne.unitValuation.RankOne.unit_ne_one · cited by 0RankOne.unit_ne_oneDFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingValuation · cited by 823ValuationLinearOrderedCommGroupWithZero · cited by 528LinearOrderedCommGroupWit…Valuation.RankOne · cited by 32Valuation.RankOneValuation.IsNontrivial.exists_val_nontrivial · cited by 2IsNontrivial.exists_val_n…RankOne.nontrivialCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.