Theorems · Theorem · commutative algebra
Ring.two_ne_zero
∀ {R : Type u_2} [inst : NonAssocSemiring R] [Nontrivial R], ringChar R ≠ 2 → 2 ≠ 0We have 2 ≠ 0 in a nontrivial ring whose characteristic is not 2.
- Defined in
- Mathlib.Algebra.CharP.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NonAssocSemiringNontrivial
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
- NonAssocSemiringstatement and proof · cited by 805
- ringCharstatement and proof · cited by 73
- Nat.prime_twoproof · cited by 55
- Nat.dvd_primeproof · cited by 18
- ringChar.specproof · cited by 7
- CharP.ringChar_ne_oneproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- Ring.neg_one_ne_one_of_char_ne_twoproof · cited by 5
- Ring.eq_self_iff_eq_zero_of_char_ne_twoproof · cited by 1
- FiniteField.isSquare_neg_two_iffproof · cited by 1
- FiniteField.two_pow_cardproof · cited by 1
- FiniteField.isSquare_two_iffproof · cited by 1