Theorems · Definition · field theory
Polynomial.leadingCoeffHom
{R : Type u} → [inst : Semiring R] → [NoZeroDivisors R] → Polynomial R →* RPolynomial.leadingCoeff bundled as a MonoidHom when R has NoZeroDivisors, and thus
leadingCoeff is multiplicative
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringNoZeroDivisors
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Polynomialstatement · cited by 5,681
- MonoidHomstatement · cited by 3,629
- NoZeroDivisorsstatement and proof · cited by 545
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.leadingCoeff_mulproof · cited by 32
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_multiset_prodproof · cited by 1
- Polynomial.leadingCoeffHom_applystatement · cited by 1
- Polynomial.leadingCoeff_powproof · cited by 1
- Polynomial.leadingCoeff_dvd_leadingCoeffproof · cited by 1
- minpoly.IsIntegrallyClosed.isIntegral_iff_isUnit_leadingCoeffproof · cited by 0
- Polynomial.leadingCoeffHom.congr_simpstatement and proof · cited by 0