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Theorems · Theorem · commutative algebra

Valuation.IsNontrivial.exists_val_nontrivial

∀ {R : Type u_3} {Γ₀ : Type u_4} {inst : Ring R} {inst_1 : LinearOrderedCommMonoidWithZero Γ₀} {v : Valuation R Γ₀}
  [self : v.IsNontrivial], ∃ x, v x ≠ 0 ∧ v x ≠ 1
Defined in
Mathlib.RingTheory.Valuation.Basic
Cited by
2 results in Mathlib
Foundations
Depth 23 from the axioms · uses propext
Assumes
Valuation.IsNontrivial
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Around this declaration

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

Valuation.RankOne.nontrivial · cited by 1RankOne.nontrivialValuation.IsNontrivial.nontrivial_codomain · cited by 0IsNontrivial.nontrivial_c…DFunLike.coe · cited by 62936DFunLike.coeRing · cited by 7463RingValuation · cited by 823ValuationLinearOrderedCommMonoidWithZero · cited by 139LinearOrderedCommMonoidWi…Valuation.IsNontrivial · cited by 27Valuation.IsNontrivialIsNontrivial.exists_val_nontr…CITED BYCITES

Cites5

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Cited by2

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