Polynomial.isPrimitive_of_contentIdeal_eq_top

∀ {R : Type u_3} [inst : CommSemiring R] {p : Polynomial R}, p.contentIdeal = ⊤ → p.IsPrimitive

If the coefficients of p generate the whole ring, then p is primitive.

Defined in: Mathlib.RingTheory.Polynomial.ContentIdeal
Cited by: 1 results in Mathlib
Foundations: Depth 105 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommSemiring

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Results whose statement or proof uses this declaration.