Theorems · Theorem · commutative algebra
CharP.char_is_prime_or_zero
∀ (R : Type u_1) [inst : NonAssocSemiring R] [NoZeroDivisors R] [Nontrivial R] (p : ℕ) [hc : CharP R p], Nat.Prime p ∨ p = 0
- Defined in
- Mathlib.Algebra.CharP.Defs
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- NonAssocSemiringstatement and proof · cited by 805
- NoZeroDivisorsstatement and proof · cited by 545
- CharPstatement and proof · cited by 478
- CharP.char_ne_oneproof · cited by 6
- CharP.char_is_prime_of_two_leproof · cited by 1
Cited by14
Results whose statement or proof uses this declaration.
- CharP.char_is_primeproof · cited by 4
- CharP.exists'proof · cited by 2
- CharP.char_is_prime_of_posproof · cited by 2
- CharP.of_ringHom_of_ne_zeroproof · cited by 2
- Polynomial.exists_separable_of_irreducibleproof · cited by 1
- IsAlgClosed.ringEquiv_of_equiv_of_char_eqproof · cited by 1
- FirstOrder.Field.charP_iff_model_fieldOfCharproof · cited by 1
- charP_zero_or_prime_powerproof · cited by 1
- MixedCharZero.reduce_to_p_primeproof · cited by 1
- ax_grothendieck_of_definableproof · cited by 1
- CharP.char_prime_of_ne_zeroproof · cited by 1
- FiniteField.card_cast_subgroup_card_ne_zeroproof · cited by 0