Theorems · Definition · commutative algebra
Ideal.absNorm
{S : Type u_1} → [inst : CommRing S] → [IsDedekindDomain S] → [Module.Free ℤ S] → Ideal S →*₀ ℕThe absolute norm of the ideal I : Ideal R is the cardinality of the quotient R ⧸ I.
- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 123 results in Mathlib
- Foundations
- Depth 153 from the axioms, rests on 5,188 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 4,748
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Submodule.cardQuotproof · cited by 14
Cited by129
Results whose statement or proof uses this declaration.
- FractionalIdeal.absNormproof · cited by 19
- Ideal.absNorm_span_singletonstatement and proof · cited by 18
- NumberField.HeightOneSpectrum.absNorm_ne_zerostatement · cited by 18
- RingOfIntegers.exponentproof · cited by 15
- NumberField.HeightOneSpectrum.one_lt_absNorm_nnrealstatement and proof · cited by 8
- NumberField.Set.primeIdealZetaSumproof · cited by 5
- Ideal.absNorm_applystatement · cited by 5
- Ideal.absNorm_dvd_absNorm_of_lestatement and proof · cited by 5
- Ideal.absNorm_memstatement · cited by 5
- Ideal.natAbs_pow_inertiaDegstatement and proof · cited by 4
- NumberField.absNorm_differentIdealstatement · cited by 4
- Ideal.finite_setOfPred_absNorm_lestatement and proof · cited by 4