Theorems · Theorem · number theory
AlgHom.IsArithFrobAt.comap_eq
∀ {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 → ∀ [Q.IsPrime], Ideal.comap φ Q = Q- Defined in
- Mathlib.RingTheory.Frobenius
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 103 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.coeproof · cited by 62,936
- 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
- HasQuotient.Quotientproof · cited by 2,301
- le_antisymmproof · cited by 2,068
- map_zeroproof · cited by 1,614
- Ideal.IsPrimestatement and proof · cited by 827
- Ideal.Quotient.mkproof · cited by 610
- Ideal.comapstatement and proof · cited by 443
- Ideal.Quotient.eq_zero_iff_memproof · cited by 74
Cited by2
Results whose statement or proof uses this declaration.
- AlgHom.IsArithFrobAt.localize_algebraMapproof · cited by 1
- IsArithFrobAt.mem_stabilizerproof · cited by 1