rank_inf_eq_one_of_flat_right_of_inj

English

If B is flat and A⊥B, then rank(A⊓B) = 1 under injectivity.

Русский

Если B плоская и A⊥B, то ранг A⊓B равен 1 при инъекции.

LaTeX

$$$B\\text{ flat} \\land A\\perp_L B \\Rightarrow \\operatorname{rank}_R(A\\cap B)=1$$$

Lean4

theorem rank_inf_eq_one_of_flat_right_of_inj [Module.Flat R B] (hinj : Function.Injective (algebraMap R S)) :
    Module.rank R ↥(A ⊓ B) = 1 :=
  H.rank_inf_eq_one_of_commute_of_flat_right_of_inj (fun _ _ ↦ mul_comm _ _) hinj

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