Theorems · Theorem · commutative algebra
frobenius_def
∀ {R : Type u_1} [inst : CommSemiring R] (p : ℕ) [inst_1 : ExpChar R p] (x : R), (frobenius R p) x = x ^ p- Defined in
- Mathlib.Algebra.CharP.Frobenius
- Cited by
- 8 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.
Cites5
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
- ExpCharstatement and proof · cited by 276
- frobeniusstatement · cited by 80
Cited by8
Results whose statement or proof uses this declaration.
- Polynomial.map_frobenius_expandproof · cited by 2
- gaussSum_frobproof · cited by 1
- MvPolynomial.frobenius_zmodproof · cited by 1
- perfectField_of_perfectClosure_eq_botproof · cited by 1
- IsPrimitiveRoot.neZero'proof · cited by 1
- FiniteField.frobenius_powproof · cited by 1
- ZMod.frobenius_zmodproof · cited by 0