Theorems · Theorem · commutative algebra
Polynomial.contentIdeal_le_contentIdeal_of_dvd
∀ {R : Type u_3} [inst : CommSemiring R] {p q : Polynomial R}, p ∣ q → q.contentIdeal ≤ p.contentIdeal- Cited by
- 1 results in Mathlib
- Foundations
- Depth 91 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Idealstatement · cited by 4,748
- le_transproof · cited by 985
- Polynomial.contentIdealstatement · cited by 24
- Ideal.mul_le_leftproof · cited by 19
- Polynomial.contentIdeal_mul_le_mul_contentIdealproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.IsPrincipal.contentIdeal_le_span_iff_dvdproof · cited by 1