Theorems · Theorem · commutative algebra
Polynomial.contentIdeal_mul_le_mul_contentIdeal
∀ {R : Type u_1} [inst : Semiring R] (p q : Polynomial R), (p * q).contentIdeal ≤ p.contentIdeal * q.contentIdeal- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
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.
- Semiringstatement and proof · cited by 13,802
- SetLike.coeproof · cited by 8,199
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- Polynomial.coeffproof · cited by 1,045
- Polynomial.supportproof · cited by 237
- Ideal.span_leproof · cited by 70
- Polynomial.coeff_mulproof · cited by 29
- Polynomial.contentIdealstatement and proof · cited by 24
- Polynomial.contentIdeal_defproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.contentIdeal_le_contentIdeal_of_dvdproof · cited by 1
- Polynomial.contentIdeal_eq_top_of_contentIdeal_mul_eq_topproof · cited by 0