Mathlib Map

Theorems · Theorem · commutative algebra

Polynomial.isPrimitive_iff_contentIdeal_eq_top

∀ {R : Type u_3} [inst : CommSemiring R] [IsBezout R] (p : Polynomial R), p.IsPrimitive ↔ p.contentIdeal = ⊤

The polynomial p is primitive if and only if the coefficients of p generate the whole ring.

Defined in
Mathlib.RingTheory.Polynomial.ContentIdeal
Cited by
1 results in Mathlib
Foundations
Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringIsBezout

Around this declaration

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

Cites10

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

Cited by1

Results whose statement or proof uses this declaration.