Theorems · Theorem · commutative algebra
Ideal.absNorm_apply
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] (I : Ideal S),
Ideal.absNorm I = Submodule.cardQuot I- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- DFunLike.coestatement · cited by 62,936
- 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
- Ideal.absNormstatement · cited by 123
- Submodule.cardQuotstatement · cited by 14
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.absNorm_memproof · cited by 5
- Ideal.absNorm_eq_one_iffproof · cited by 4
- NumberField.exists_ideal_in_class_of_norm_leproof · cited by 1
- IsPrimitiveRoot.card_quotient_toInteger_sub_oneproof · cited by 1
- Int.absNorm_under_dvd_absNormproof · cited by 0