Theorems · Theorem · commutative algebra
charP_zero_or_prime_power
∀ (R : Type u_1) [inst : CommRing R] [IsLocalRing R] (q : ℕ) [char_R_q : CharP R q], q = 0 ∨ IsPrimePow q
In a local ring the characteristic is either zero or a prime power.
- Defined in
- Mathlib.Algebra.CharP.LocalRing
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRingIsLocalRingCharP
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- one_mulproof · cited by 2,841
- HasQuotient.Quotientproof · cited by 2,301
- mul_commproof · cited by 2,262
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.Primeproof · cited by 2,059
- Units.valproof · cited by 1,966
- mul_assocproof · cited by 1,667
- IsUnitproof · cited by 1,602
- pow_zeroproof · cited by 1,094
- CharZeroproof · cited by 932
Cited by1
Results whose statement or proof uses this declaration.
- split_by_characteristic_localRingproof · cited by 0