Theorems · Theorem · field theory
pNilradical_eq_bot_of_frobenius_inj
∀ (R : Type u_1) [inst : CommSemiring R] (p : ℕ) [inst_1 : ExpChar R p], Function.Injective ⇑(frobenius R p) → pNilradical R p = ⊥
- Defined in
- Mathlib.FieldTheory.IsPerfectClosure
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 97 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Idealstatement · cited by 4,748
- Bot.botstatement and proof · cited by 4,720
- map_zeroproof · cited by 1,614
- ExpCharstatement and proof · cited by 276
- frobeniusstatement and proof · cited by 80
- bot_uniqueproof · cited by 57
- iterateFrobeniusproof · cited by 39
- Ideal.mem_botproof · cited by 21
- pNilradicalstatement · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- PerfectRing.pNilradical_eq_botproof · cited by 1