Theorems · Theorem · commutative algebra
Ideal.norm_dvd_iff
∀ {S : Type u_1} [inst : CommRing S] [IsDedekindDomain S] [Module.Free ℤ S] [Module.Finite ℤ S] {x : S},
Prime ((Algebra.norm ℤ) x) → ∀ {y : ℤ}, (Algebra.norm ℤ) x ∣ y ↔ x ∣ ↑y- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
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
- CommRingstatement and proof · cited by 17,173
- Idealproof · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Nat.Primeproof · cited by 2,059
- Module.Finitestatement and proof · cited by 1,032
- Ideal.spanproof · cited by 948
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Primestatement and proof · cited by 277
- Algebra.normstatement and proof · cited by 155
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.Rat.zeta_sub_one_dvd_intCast_iffproof · cited by 1
- IsPrimitiveRoot.toInteger_sub_one_dvd_primeproof · cited by 1
- IsPrimitiveRoot.toInteger_sub_one_not_dvd_twoproof · cited by 1