Theorems · Theorem · commutative algebra
CharZero.charZero_iff_forall_prime_ne_zero
∀ (R : Type u_1) [inst : NonAssocRing R] [NoZeroDivisors R] [Nontrivial R], CharZero R ↔ ∀ (p : ℕ), Nat.Prime p → ↑p ≠ 0
- Defined in
- Mathlib.Algebra.CharP.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nontrivialstatement and proof · cited by 2,416
- Nat.Primestatement and proof · cited by 2,059
- CharZerostatement and proof · cited by 932
- NoZeroDivisorsstatement and proof · cited by 545
- NonAssocRingstatement and proof · cited by 483
- CharPproof · cited by 478
- CharP.cast_eq_zeroproof · cited by 357
- Nat.Prime.ne_zeroproof · cited by 109
- ringCharproof · cited by 73
- CharP.char_is_prime_or_zeroproof · cited by 14
- CharP.charP_to_charZeroproof · cited by 11
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