Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.mem_integers_of_valuation_le_one
∀ {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] (x : K),
(∀ (v : IsDedekindDomain.HeightOneSpectrum R), (IsDedekindDomain.HeightOneSpectrum.valuation K v) x ≤ 1) →
x ∈ (algebraMap R K).range- Cited by
- 1 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- Algebra.algebraMapstatement and proof · cited by 4,706
- add_zeroproof · cited by 2,707
- Multisetproof · cited by 2,627
- mul_commproof · cited by 2,262
- map_zeroproof · cited by 1,614
- map_mulproof · cited by 1,137
Cited by1
Results whose statement or proof uses this declaration.
- IsDedekindDomain.integer_emptyproof · cited by 0