Theorems · Theorem · commutative algebra
RingHom.frobenius_comm
∀ {R : Type u_1} [inst : CommSemiring R] {S : Type u_2} [inst_1 : CommSemiring S] (g : R →+* S) (p : ℕ)
[inst_2 : ExpChar R p] [inst_3 : ExpChar S p], g.comp (frobenius R p) = (frobenius S p).comp gThe Frobenius endomorphism commutes with any ring homomorphism.
- Defined in
- Mathlib.Algebra.CharP.Frobenius
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- RingHom.compstatement · cited by 899
- RingHom.extproof · cited by 331
- ExpCharstatement and proof · cited by 276
- frobeniusstatement · cited by 80
- RingHom.map_frobeniusproof · cited by 2
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