Mathlib Map

Theorems · Definition · commutative algebra

IsDedekindDomain.HeightOneSpectrum.intValuation

{R : Type u_1} →
  [inst : CommRing R] →
    [IsDedekindDomain R] → IsDedekindDomain.HeightOneSpectrum R → Valuation R (WithZero (Multiplicative ℤ))

The v-adic valuation on R.

Defined in
Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by
53 results in Mathlib
Foundations
Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDedekindDomain
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsDedekindDomain.HeightOneSpectrum.valuation · cited by 130HeightOneSpectrum.valuati…IsDedekindDomain.HeightOneSpectrum.valuation_of_algebraMap · cited by 23HeightOneSpectrum.valuati…IsDedekindDomain.HeightOneSpectrum.intValuation_if_neg · cited by 11HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_le_one · cited by 9HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvd · cited by 5HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.valuation_of_mk' · cited by 4HeightOneSpectrum.valuati…IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero' · cited by 4HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intAdicAbv_lt_one_iff · cited by 3HeightOneSpectrum.intAdic…LaurentSeries.intValuation_le_iff_coeff_lt_eq_zero · cited by 3LaurentSeries.intValuatio…IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizer · cited by 3HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvd · cited by 3HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_mem · cited by 3HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero · cited by 3HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation_singleton · cited by 3HeightOneSpectrum.intValu…IsDiscreteValuationRing.intValuation_maximalIdeal · cited by 3IsDiscreteValuationRing.i…CommRing · cited by 17173CommRingMultiplicative · cited by 875MultiplicativeValuation · cited by 823ValuationIsDedekindDomain · cited by 668IsDedekindDomainWithZero · cited by 586WithZeroIsDedekindDomain.HeightOneSpectrum · cited by 338IsDedekindDomain.HeightOn…IsDedekindDomain.HeightOneSpectrum.intValuationDef · cited by 9HeightOneSpectrum.intValu…IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max' · cited by 0intValuation.map_add_le_m…IsDedekindDomain.HeightOneSpectrum.intValuation.map_mul' · cited by 0intValuation.map_mul'IsDedekindDomain.HeightOneSpectrum.intValuation.map_one' · cited by 0intValuation.map_one'IsDedekindDomain.HeightOneSpectrum.intValuation.map_zero' · cited by 0intValuation.map_zero'HeightOneSpectrum.intValuationCITED BYCITES

Cites11

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Cited by55

Results whose statement or proof uses this declaration.