Theorems · Definition · commutative algebra
RatFunc.polynomialValuationX
(K : Type u_2) → [inst : Field K] → Valuation (RatFunc K) (WithZero (Multiplicative ℤ))
polynomialValuationX is an abbreviation for the X-adic valuation given by
(Polynomial.idealX K).valuation K⟮X⟯.
- Defined in
- Mathlib.RingTheory.LaurentSeries
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Multiplicativestatement · cited by 875
- Valuationstatement · cited by 823
- WithZerostatement · cited by 586
- RatFuncstatement and proof · cited by 301
- IsDedekindDomain.HeightOneSpectrum.valuationproof · cited by 130
- Polynomial.idealXproof · cited by 23
Cited by14
Results whose statement or proof uses this declaration.
- LaurentSeries.LaurentSeriesPkgstatement and proof · cited by 6
- LaurentSeries.ratfuncAdicComplPkgstatement · cited by 4
- LaurentSeries.valuation_compareproof · cited by 3
- RatFunc.valuation_eq_LaurentSeries_valuationstatement · cited by 2
- LaurentSeries.continuous_coe'statement · cited by 1
- LaurentSeries.extensionAsRingHomstatement and proof · cited by 1
- LaurentSeries.LaurentSeries_coestatement and proof · cited by 1
- LaurentSeries.ratfuncAdicComplRingEquiv_applystatement · cited by 1
- LaurentSeries.uniformContinuous_withVal_equivstatement · cited by 1
- LaurentSeries.valuation_LaurentSeries_equal_extensionstatement and proof · cited by 1
- LaurentSeries.valuation_coe_ratFuncproof · cited by 1
- LaurentSeries.coe_X_compareproof · cited by 0