Theorems · Theorem · commutative algebra
CharP.char_ne_zero_of_finite
∀ (R : Type u_1) [inst : NonAssocRing R] (p : ℕ) [CharP R p] [Finite R], p ≠ 0
The characteristic of a finite ring cannot be zero.
- Defined in
- Mathlib.Algebra.CharP.Lemmas
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocRingCharPFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finitestatement and proof · cited by 3,029
- CharZeroproof · cited by 932
- NonAssocRingstatement and proof · cited by 483
- CharPstatement and proof · cited by 478
- Nat.cast_injectiveproof · cited by 39
- CharP.charP_to_charZeroproof · cited by 11
- not_injective_infinite_finiteproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- CharP.char_is_primeproof · cited by 4
- isUnit_iff_not_dvd_charproof · cited by 4
- CharP.ringChar_ne_zero_of_finiteproof · cited by 1