Theorems · Definition · commutative algebra

MvPolynomial.universalFactorizationMapLiftEquiv

(R : Type u_1) →
  (S : Type u_2) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] →
          (n m k : ℕ) →
            (hn : n = m + k) →
              (p : Polynomial.MonicDegreeEq S n) →
                { f //
                    f.comp (MvPolynomial.universalFactorizationMap R n m k hn) =
                      (MvPolynomial.mapEquivMonic R S n).symm p } ≃
                  { q // ↑q.1 * ↑q.2 = ↑p }

Lifts along universalFactorizationMap corresponds to factorization of p into monic polynomials with fixed degrees.

Defined in

Mathlib.RingTheory.Polynomial.UniversalFactorizationRing

Cited by

1 results in Mathlib

Foundations

Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebra