quotientEquivPiFactors_mk — Mathlib

English

A corollary of the product decomposition: the quotient by a product of prime powers is isomorphic to the product of the quotients by each prime power, and this holds in a Dedekind domain.

Русский

Следствие разложения на произведение: квадрат по простым степеням задаёт изоморфизм кольца тождеств, аналогично каждому члену произведения.

LaTeX

$$$R/I \cong \prod_{i} R/P_i^{e_i} \text{ where } I = \prod_i P_i^{e_i}$$$

Lean4

@[simp]
theorem quotientEquivPiFactors_mk {I : Ideal R} (hI : I ≠ ⊥) (x : R) :
    IsDedekindDomain.quotientEquivPiFactors hI (Ideal.Quotient.mk I x) = fun _P => Ideal.Quotient.mk _ x :=
  rfl

Похожие утверждения