Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.associates_irreducible
∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R),
Irreducible (Associates.mk v.asIdeal)- Cited by
- 11 results in Mathlib
- Foundations
- Depth 149 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- IsDedekindDomainstatement and proof · cited by 668
- Irreduciblestatement · cited by 496
- IsDedekindDomain.HeightOneSpectrumstatement and proof · cited by 338
- Associatesstatement · cited by 210
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- Associates.mkstatement · cited by 137
- IsDedekindDomain.HeightOneSpectrum.irreducibleproof · cited by 13
- Associates.irreducible_mkproof · cited by 11
Cited by11
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intValuation_le_pow_iff_dvdproof · cited by 5
- FractionalIdeal.count_mulproof · cited by 4
- IsDedekindDomain.HeightOneSpectrum.intValuation_exists_uniformizerproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.intValuation_singletonproof · cited by 3
- FractionalIdeal.count_selfproof · cited by 3
- FractionalIdeal.count_maximal_coprimeproof · cited by 2
- FractionalIdeal.count_coeproof · cited by 1
- Ideal.finprod_countproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation.map_add_le_max'proof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.intValuation.map_mul'proof · cited by 0
- IsDedekindDomain.HeightOneSpectrum.intValuation.map_one'proof · cited by 0