Theorems · Theorem · commutative algebra
Ideal.absNorm_mem
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] (I : Ideal S),
↑(Ideal.absNorm I) ∈ I- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- HasQuotient.Quotientproof · cited by 2,301
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Ideal.Quotient.mkproof · cited by 610
- Module.Freestatement and proof · cited by 597
- map_natCastproof · cited by 134
- Ideal.absNormstatement · cited by 123
- Submodule.toAddSubgroupproof · cited by 106
- AddSubgroup.indexproof · cited by 104
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.span_singleton_absNormproof · cited by 1
- Ideal.span_singleton_absNorm_leproof · cited by 1
- Ideal.exists_prime_and_absNorm_eq_powproof · cited by 1
- IsCyclotomicExtension.Rat.p_mem_span_zeta_sub_oneproof · cited by 1
- NumberField.discr_mem_differentIdealproof · cited by 1