mvPolynomialQuotientEquiv — Mathlib

English

The homogeneousSubmodule construction forms a gradedMonoid structure; the grading is compatible with multiplication.

Русский

Конструкция однородных подмодулей образует градаированный моноид; градация совместима с умножением.

LaTeX

$$gradedMonoid : SetLike.GradedMonoid (homogeneousSubmodule σ R)$$

Lean4

/-- The canonical algebra isomorphism from `MvPolynomial Unit R` quotiented by
`C r * X () - 1` to the localization of `R` away from `r`. -/
noncomputable def mvPolynomialQuotientEquiv : ((MvPolynomial Unit R) ⧸ Ideal.span {C r * X () - 1}) ≃ₐ[R] S
    where
  toFun := auxHom S r
  invFun := auxInv S r
  left_inv x := by simpa using congrFun (congrArg DFunLike.coe <| auxInv_auxHom S r) x
  right_inv s := by simpa using congrFun (congrArg DFunLike.coe <| auxHom_auxInv S r) s
  map_mul' := by simp
  map_add' := by simp
  commutes' := by simp

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