Theorems · Theorem · commutative algebra
IsDedekindDomain.HeightOneSpectrum.irreducible
∀ {R : Type u_1} [inst : CommRing R] [IsDedekindDomain R] (v : IsDedekindDomain.HeightOneSpectrum R),
Irreducible v.asIdeal- Cited by
- 13 results in Mathlib
- Foundations
- Depth 148 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.
Cites8
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
- IsDedekindDomain.HeightOneSpectrum.asIdealstatement · cited by 156
- UniqueFactorizationMonoid.irreducible_iff_primeproof · cited by 8
- IsDedekindDomain.HeightOneSpectrum.primeproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.associates_irreducibleproof · cited by 11
- FractionalIdeal.count_well_definedproof · cited by 5
- IsDedekindDomain.HeightOneSpectrum.intValuation_lt_one_iff_dvdproof · cited by 3
- IsDedekindDomain.HeightOneSpectrum.maxPowDividing_eq_pow_multiset_countproof · cited by 2
- IsDedekindDomain.HeightOneSpectrum.intValuation_eq_exp_neg_multiplicityproof · cited by 2
- Ideal.map_algebraMap_eq_finsetProd_powproof · cited by 2
- FractionalIdeal.finite_factors'proof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.intValuation_liesOverproof · cited by 1
- NumberField.FinitePlace.prod_eq_inv_abs_norm_intproof · cited by 1
- Associates.finite_factorsproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.exists_intValuation_mul_sub_ltproof · cited by 1