Theorems · Theorem · commutative algebra
isUnit_iff_not_dvd_char_of_ringChar_ne_zero
∀ (R : Type u_1) [inst : CommRing R] (p : ℕ) [Fact (Nat.Prime p)], ringChar R ≠ 0 → (IsUnit ↑p ↔ ¬p ∣ ringChar R)
A prime p is a unit in a commutative ring R of nonzero characteristic iff it does not divide
the characteristic.
- Defined in
- Mathlib.Algebra.CharP.CharAndCard
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- mul_oneproof · cited by 3,885
- Factstatement and proof · cited by 2,726
- add_zeroproof · cited by 2,707
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.Primestatement and proof · cited by 2,059
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- Int.cast_natCastproof · cited by 393
- Int.cast_oneproof · cited by 371
- CharP.cast_eq_zeroproof · cited by 357
Cited by1
Results whose statement or proof uses this declaration.
- isUnit_iff_not_dvd_charproof · cited by 4