Theorems · Theorem · commutative algebra
Ideal.isPrime_of_irreducible_absNorm
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] {I : Ideal S},
Irreducible (Ideal.absNorm I) → I.IsPrime- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimestatement · cited by 827
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Irreduciblestatement and proof · cited by 496
- Ideal.absNormstatement and proof · cited by 123
- Ideal.isPrime_of_primeproof · cited by 17
- UniqueFactorizationMonoid.irreducible_iff_primeproof · cited by 8
- Ideal.irreducible_of_irreducible_absNormproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.prime_of_irreducible_absNorm_spanproof · cited by 2