Theorems · Theorem · field theory

Polynomial.irreducible_of_monic

∀ {R : Type u} [inst : CommSemiring R] [NoZeroDivisors R] {p : Polynomial R},
  p.Monic → p ≠ 1 → (Irreducible p ↔ ∀ (f g : Polynomial R), f.Monic → g.Monic → f * g = p → f = 1 ∨ g = 1)

Defined in

Mathlib.Algebra.Polynomial.Monic

Cited by

3 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringNoZeroDivisors