Theorems · Theorem · commutative algebra
Ideal.prime_of_irreducible_absNorm_span
∀ {S : Type u_1} [inst : CommRing S] [inst_1 : IsDedekindDomain S] [inst_2 : Module.Free ℤ S] {a : S},
a ≠ 0 → Irreducible (Ideal.absNorm (Ideal.span {a})) → Prime a- Defined in
- Mathlib.RingTheory.Ideal.Norm.AbsNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.Freestatement and proof · cited by 597
- Irreduciblestatement and proof · cited by 496
- Primestatement · cited by 277
- Ideal.absNormstatement and proof · cited by 123
- Ideal.span_singleton_primeproof · cited by 27
Cited by2
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.zeta_sub_one_prime_of_ne_twoproof · cited by 1
- IsPrimitiveRoot.zeta_sub_one_prime_of_two_powproof · cited by 1