Theorems · Theorem · number theory
AlgHom.IsArithFrobAt.card_pos
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {φ : S →ₐ[R] S}
{Q : Ideal S}, φ.IsArithFrobAt Q → 0 < Nat.card (R ⧸ Ideal.under R Q)- Defined in
- Mathlib.RingTheory.Frobenius
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement and proof · cited by 4,748
- AlgHomstatement and proof · cited by 3,236
- Finiteproof · cited by 3,029
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Nat.cardstatement · cited by 844
- Ideal.understatement and proof · cited by 170
- Nat.card_posproof · cited by 36
- AlgHom.IsArithFrobAtstatement and proof · cited by 13
- AlgHom.IsArithFrobAt.finite_quotientproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- AlgHom.IsArithFrobAt.restrict_injectiveproof · cited by 1
- AlgHom.IsArithFrobAt.le_comapproof · cited by 1