exact_smul_id_smul_top_mkQ — Mathlib

English

For any ideal I, the Rees algebra I has FG property; i.e., (reesAlgebra I).FG.

Русский

Для любого идеала I выполняется: Rees-алгебра I конечного типа; (reesAlgebra I).FG.

LaTeX

$$$(\mathrm{reesAlgebra}(I)).FG$$$

Lean4

theorem exact_smul_id_smul_top_mkQ (M : Type v) [AddCommGroup M] [Module R M] (r : R) :
    Function.Exact (r • LinearMap.id : M →ₗ[R] M) (r • (⊤ : Submodule R M)).mkQ :=
  by
  intro x
  simp [Submodule.mem_smul_pointwise_iff_exists, Submodule.mem_smul_pointwise_iff_exists]

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