Theorems · Definition · number theory

IsArithFrobAt

(R : Type u_1) →
  {S : Type u_2} →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          {M : Type u_3} →
            [inst_3 : Monoid M] → [inst_4 : MulSemiringAction M S] → [SMulCommClass M R S] → M → Ideal S → Prop

Suppose S is an R algebra, M is a monoid acting on S whose action is trivial on R σ : M is an (arithmetic) Frobenius at an ideal Q of S if σ • x ≡ x ^ q (mod Q) for all x.

Defined in

Mathlib.RingTheory.Frobenius

Cited by

6 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraMonoidMulSemiringActionSMulCommClass