Theorems · Definition · commutative algebra
IsDedekindDomain.HeightOneSpectrum.intAdicAbvDef
{R : Type u_1} →
[inst : CommRing R] → [IsDedekindDomain R] → IsDedekindDomain.HeightOneSpectrum R → {b : NNReal} → 1 < b → R → NNRealThe v-adic absolute value function on R defined as b raised to negative v-adic
valuation, for some b in ℝ≥0
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsDedekindDomain
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.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- NNRealstatement and proof · cited by 4,310
- IsDedekindDomainstatement and proof · cited by 668
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- IsDedekindDomain.HeightOneSpectrum.intValuationproof · cited by 53
- WithZeroMulInt.toNNRealproof · cited by 28
Cited by2
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intAdicAbvproof · cited by 11
- IsDedekindDomain.HeightOneSpectrum.isNonarchimedean_intAdicAbvDefstatement · cited by 1