Theorems · Definition · commutative algebra
HahnSeries.addVal
(Γ : Type u_1) →
(R : Type u_2) →
[inst : AddCancelCommMonoid Γ] →
[inst_1 : LinearOrder Γ] →
[inst_2 : IsOrderedCancelAddMonoid Γ] →
[inst_3 : Ring R] → [IsDomain R] → AddValuation (HahnSeries Γ R) (WithTop Γ)The additive valuation on R⟦Γ⟧ returning the smallest index at which
a Hahn Series has a nonzero coefficient, or ⊤ for the 0 series.
- Defined in
- Mathlib.RingTheory.HahnSeries.Valuation
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LinearOrderstatement and proof · cited by 8,572
- Ringstatement and proof · cited by 7,463
- WithTopstatement · cited by 3,754
- IsDomainstatement and proof · cited by 2,196
- HahnSeriesstatement and proof · cited by 528
- IsOrderedCancelAddMonoidstatement and proof · cited by 359
- HahnSeries.orderTopproof · cited by 103
- AddValuationstatement · cited by 96
- AddCancelCommMonoidstatement and proof · cited by 48
- AddValuation.ofproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- HahnSeries.addVal_applystatement · cited by 1
- HahnSeries.addVal_apply_of_nestatement · cited by 0
- HahnSeries.addVal_le_of_coeff_ne_zerostatement · cited by 0