Theorems · Theorem · commutative algebra

ModP.mul_ne_zero_of_pow_p_ne_zero

∀ {K : Type u₁} [inst : Field K] {v : Valuation K NNReal} {O : Type u₂} [inst_1 : CommRing O] [inst_2 : Algebra O K],
  v.Integers O → ∀ {p : ℕ} [hp : Fact (Nat.Prime p)] {x y : ModP O p}, x ^ p ≠ 0 → y ^ p ≠ 0 → x * y ≠ 0

Defined in

Mathlib.RingTheory.Perfection

Cited by

1 results in Mathlib

Foundations

Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCommRingAlgebraFact