Theorems · Theorem · commutative algebra
Ideal.natAbs_pow_inertiaDeg
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] [inst_2 : Module.Free ℤ R] [Module.Finite ℤ R]
(p : ℤ) (P : Ideal R) [P.IsPrime] [P.LiesOver (Ideal.span {p})], p.natAbs ^ P.inertiaDeg ℤ = Ideal.absNorm P- Cited by
- 4 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement and proof · cited by 4,748
- Module.Finitestatement and proof · cited by 1,032
- Ideal.spanstatement and proof · cited by 948
- Ideal.IsPrimestatement and proof · cited by 827
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Ideal.LiesOverstatement and proof · cited by 272
- Ideal.absNormstatement and proof · cited by 123
Cited by4
Results whose statement or proof uses this declaration.
- Ideal.pow_inertiaDegproof · cited by 3
- NumberField.not_dvd_discr_iff_forall_liesOverproof · cited by 2
- Ideal.natAbs_pow_inertiaDeg'proof · cited by 0