Theorems · Theorem · number theory
IsArithFrobAt.exists_primesOver_isConj
∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (G : Type u_3)
[inst_3 : Group G] [inst_4 : MulSemiringAction G S] [inst_5 : SMulCommClass G R S] [Finite G]
[Algebra.IsInvariant R S G] (P : Ideal R),
(∃ Q, Finite (S ⧸ ↑Q)) →
∃ σ, (∀ (Q : ↑(P.primesOver S)), IsArithFrobAt R (σ Q) ↑Q) ∧ ∀ (Q₁ Q₂ : ↑(P.primesOver S)), IsConj (σ Q₁) (σ Q₂)- Defined in
- Mathlib.RingTheory.Frobenius
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Idealstatement and proof · cited by 4,748
- Finitestatement and proof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- SMulCommClassstatement and proof · cited by 1,927
- Ideal.IsPrimeproof · cited by 827
- MulSemiringActionstatement and proof · cited by 423
- Ideal.LiesOverproof · cited by 272
Cited by2
Results whose statement or proof uses this declaration.
- IsArithFrobAt.arithFrobAtproof · cited by 1
- isConj_arithFrobAtproof · cited by 0