Theorems · Theorem · commutative algebra
ringChar.spec
∀ (R : Type u_1) [inst : NonAssocSemiring R] (x : ℕ), ↑x = 0 ↔ ringChar R ∣ x
- Defined in
- Mathlib.Algebra.CharP.Defs
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- NonAssocSemiringstatement and proof · cited by 805
- CharPproof · cited by 478
- ringCharstatement and proof · cited by 73
- CharP.cast_eq_zero_iffproof · cited by 42
- CharP.existsUniqueproof · cited by 2
Cited by7
Results whose statement or proof uses this declaration.
- Ring.two_ne_zeroproof · cited by 5
- ringChar.dvdproof · cited by 3
- ringChar.Nat.cast_ringCharproof · cited by 1
- ZMod.minOrderproof · cited by 1
- charP_zero_or_prime_powerproof · cited by 1
- ringChar.ringChar_eq_oneproof · cited by 0
- not_ringChar_dvd_of_invertibleproof · cited by 0