Theorems · Theorem · commutative algebra
Valuation.IsTrivialOn.valuation_algebraMap_le_one
∀ {Γ₀ : Type u_4} [inst : LinearOrderedCommMonoidWithZero Γ₀] {B : Type u_7} {A : Type u_8} [inst_1 : CommSemiring A]
[inst_2 : Ring B] [inst_3 : Algebra A B] (v : Valuation B Γ₀) [Valuation.IsTrivialOn A v] (a : A),
v ((algebraMap A B) a) ≤ 1- Defined in
- Mathlib.RingTheory.Valuation.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement · cited by 4,706
- Valuationstatement and proof · cited by 823
- LinearOrderedCommMonoidWithZerostatement and proof · cited by 139
- Valuation.IsTrivialOnstatement and proof · cited by 28
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