Theorems · Theorem · field theory
Polynomial.Monic.mul
∀ {R : Type u} [inst : Semiring R] {p q : Polynomial R}, p.Monic → q.Monic → (p * q).Monic- Defined in
- Mathlib.Algebra.Polynomial.Monic
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 92 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.
Cites8
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 and proof · cited by 5,681
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Polynomial.leadingCoeffproof · cited by 498
- Polynomial.Monicstatement and proof · cited by 461
- Polynomial.Monic.defproof · cited by 18
- Polynomial.leadingCoeff_mul'proof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.monic_multiset_prod_of_monicproof · cited by 6
- Polynomial.IsMonicOfDegree.mulproof · cited by 2
- Polynomial.cyclotomic_expand_eq_cyclotomic_mulproof · cited by 2
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_auxproof · cited by 1
- IsLocalization.Away.isIntegral_of_isIntegral_mapproof · cited by 1
- Polynomial.IsDistinguishedAt.mulproof · cited by 1
- IsIntegral.pairproof · cited by 1