Mathlib Map

Theorems · Definition · commutative algebra

MvPolynomial.mapEquivMonic

(R : Type u_1) →
  (S : Type u_2) →
    [inst : CommRing R] →
      [inst_1 : CommRing S] →
        [inst_2 : Algebra R S] → (n : ℕ) → (MvPolynomial (Fin n) R →ₐ[R] S) ≃ Polynomial.MonicDegreeEq S n

MonicDegreeEq · n is representable by R[X₁,...,Xₙ], with the universal element being freeMonic.

Defined in
Mathlib.RingTheory.Polynomial.UniversalFactorizationRing
Cited by
10 results in Mathlib
Foundations
Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MvPolynomial.universalFactorizationMap · cited by 19MvPolynomial.universalFac…MvPolynomial.coe_mapEquivMonic_comp · cited by 2MvPolynomial.coe_mapEquiv…MvPolynomial.pderiv_inl_universalFactorizationMap_X · cited by 1MvPolynomial.pderiv_inl_u…MvPolynomial.pderiv_inr_universalFactorizationMap_X · cited by 1MvPolynomial.pderiv_inr_u…MvPolynomial.universalFactorizationMapLiftEquiv · cited by 1MvPolynomial.universalFac…MvPolynomial.mapEquivMonic_symm_map · cited by 1MvPolynomial.mapEquivMoni…MvPolynomial.universalFactorizationMap_freeMonic · cited by 1MvPolynomial.universalFac…MvPolynomial.coe_mapEquivMonic_comp' · cited by 1MvPolynomial.coe_mapEquiv…Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap · cited by 1UniversalFactorizationRin…Polynomial.UniversalFactorizationRing.fromTensor_comp_universalFactorizationMap' · cited by 1UniversalFactorizationRin…Polynomial.UniversalFactorizationRing.jacobian_resentation · cited by 1UniversalFactorizationRin…MvPolynomial.mapEquivMonic_symm_map_algebraMap · cited by 0MvPolynomial.mapEquivMoni…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraEquiv · cited by 8337EquivFinsupp · cited by 5255FinsuppAlgHom · cited by 3236AlgHomMvPolynomial · cited by 2140MvPolynomialPolynomial.coeff · cited by 1045Polynomial.coeffAlgHom.toRingHom · cited by 490AlgHom.toRingHomMvPolynomial.aeval · cited by 298MvPolynomial.aevalPolynomial.MonicDegreeEq · cited by 22Polynomial.MonicDegreeEqPolynomial.MonicDegreeEq.map · cited by 12MonicDegreeEq.mapPolynomial.MonicDegreeEq.freeMonic · cited by 4MonicDegreeEq.freeMonicMvPolynomial.mapEquivMonicCITED BYCITES

Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by12

Results whose statement or proof uses this declaration.