Theorems · Theorem · commutative algebra
Ideal.leadingCoeff_mul_le
∀ {R : Type u} [inst : CommSemiring R] [NoZeroDivisors R] (I J : Ideal (Polynomial R)),
I.leadingCoeff * J.leadingCoeff ≤ (I * J).leadingCoeff- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringNoZeroDivisors
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.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- NoZeroDivisorsstatement and proof · cited by 545
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.leadingCoeff_mulproof · cited by 32
- Ideal.mul_mem_mulproof · cited by 29
- Ideal.mul_leproof · cited by 11
- Ideal.leadingCoeffstatement and proof · cited by 8
- Ideal.mem_leadingCoeffproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.leadingCoeff_finset_prod_leproof · cited by 1