Theorems · Theorem · commutative algebra
Valuation.RankOne.hom_eq_zero_iff
∀ {R : Type u_1} {Γ₀ : Type u_2} [inst : Ring R] [inst_1 : LinearOrderedCommGroupWithZero Γ₀] (v : Valuation R Γ₀)
[hv : v.RankOne] {x : (MonoidWithZeroHom.ofClass v).ValueGroup₀}, (Valuation.RankOne.hom v) x = 0 ↔ x = 0If v is a rank one valuation, then x : Γ₀ has image 0 under RankOne.hom v if and
only if x = 0.
- Defined in
- Mathlib.RingTheory.Valuation.RankOne
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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- Ringstatement and proof · cited by 7,463
- NNRealstatement and proof · cited by 4,310
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- Unitsstatement · cited by 2,804
- map_zeroproof · cited by 1,614
- Valuationstatement and proof · cited by 823
- MonoidWithZeroHomstatement · cited by 704
- LinearOrderedCommGroupWithZerostatement and proof · cited by 528
- MonoidWithZeroHom.ofClassstatement and proof · cited by 204
- MonoidWithZeroHom.valueGroupstatement · cited by 170
- MonoidWithZeroHom.ValueGroup₀statement and proof · cited by 166
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