Theorems · Theorem · commutative algebra
isUnit_iff_not_dvd_char
∀ (R : Type u_1) [inst : CommRing R] (p : ℕ) [Fact (Nat.Prime p)] [Finite R], IsUnit ↑p ↔ ¬p ∣ ringChar R
A prime p is a unit in a finite commutative ring R
iff it does not divide the characteristic.
- Defined in
- Mathlib.Algebra.CharP.CharAndCard
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finitestatement and proof · cited by 3,029
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- IsUnitstatement · cited by 1,602
- ringCharstatement and proof · cited by 73
- CharP.char_ne_zero_of_finiteproof · cited by 3
- isUnit_iff_not_dvd_char_of_ringChar_ne_zeroproof · cited by 1
Cited by4
Results whose statement or proof uses this declaration.
- FiniteField.two_pow_cardproof · cited by 1
- Char.card_pow_cardproof · cited by 1
- prime_dvd_char_iff_dvd_cardproof · cited by 1
- not_isUnit_prime_of_dvd_cardproof · cited by 1