Theorems · Theorem · commutative algebra

IsDedekindDomain.HeightOneSpectrum.coe_mem_adicCompletionIntegers

∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] {K : Type u_2} [inst_2 : Field K]
  [inst_3 : Algebra R K] [inst_4 : IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) (r : R),
  ↑r ∈ IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegers K v

A global integer is in the local integers.

Defined in: Mathlib.RingTheory.DedekindDomain.AdicValuation
Cited by: 0 results in Mathlib
Foundations: Depth 184 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDedekindDomain Field Algebra IsFractionRing

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CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Fieldstatement and proof · cited by 7,404
Multiplicativeproof · cited by 875
IsFractionRingstatement and proof · cited by 738
IsDedekindDomainstatement and proof · cited by 668
WithZeroproof · cited by 586
IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
ValuationSubringstatement · cited by 187
IsDedekindDomain.HeightOneSpectrum.adicCompletionstatement · cited by 93
Algebra.caststatement · cited by 58
IsDedekindDomain.HeightOneSpectrum.adicCompletionIntegersstatement · cited by 22

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