Theorems · Theorem · commutative algebra
frobenius_inj
∀ (R : Type u_1) [inst : CommRing R] [IsReduced R] (p : ℕ) [inst_2 : ExpChar R p], Function.Injective ⇑(frobenius R p)
- Defined in
- Mathlib.Algebra.CharP.Reduced
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement · cited by 10,189
- ExpCharstatement and proof · cited by 276
- IsReducedstatement and proof · cited by 98
- frobeniusstatement · cited by 80
- iterateFrobenius_oneproof · cited by 7
- iterateFrobenius_injproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- FiniteField.Matrix.charpoly_pow_cardproof · cited by 2
- PerfectRing.ofSurjectiveproof · cited by 2
- isSquare_of_charTwo'proof · cited by 1
- IsPrimitiveRoot.neZero'proof · cited by 1
- PerfectClosure.eq_iffproof · cited by 0