Theorems · Theorem · commutative algebra
char_eq_expChar_iff
∀ (R : Type u_1) [inst : AddMonoidWithOne R] (p q : ℕ) [hp : CharP R p] [hq : ExpChar R q], p = q ↔ Nat.Prime p
The characteristic equals the exponential characteristic iff the former is prime.
- Defined in
- Mathlib.Algebra.CharP.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddMonoidWithOneCharPExpChar
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Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.Primestatement and proof · cited by 2,059
- CharZeroproof · cited by 932
- CharPstatement and proof · cited by 478
- AddMonoidWithOnestatement and proof · cited by 313
- ExpCharstatement and proof · cited by 276
- ExpChar.casesOnproof · cited by 21
- CharP.eqproof · cited by 9
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