Theorems · Theorem · commutative algebra
iterate_frobenius
∀ {R : Type u_1} [inst : CommSemiring R] (p n : ℕ) [inst_1 : ExpChar R p] (x : R), (⇑(frobenius R p))^[n] x = x ^ p ^ n- Defined in
- Mathlib.Algebra.CharP.Frobenius
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringExpChar
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Nat.iteratestatement · cited by 740
- ExpCharstatement and proof · cited by 276
- frobeniusstatement · cited by 80
- pow_iterateproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- FiniteField.Matrix.charpoly_pow_cardproof · cited by 2
- PerfectClosure.mk_powproof · cited by 1
- iterateFrobenius_eq_powproof · cited by 1