pointwiseCentralScalar — Mathlib

English

If p contains s • N and is closed under smul by S, then s • N = p.

Русский

Если p содержит s • N и замкнута по smul от S, то s • N = p.

LaTeX

$$$s \\cdot N = p \\quad\\text{if}\\quad p \\text{ is closed under } S \\text{ and } s \\cdot N \\le p$$$

Lean4

instance pointwiseCentralScalar [DistribMulAction αᵐᵒᵖ M] [SMulCommClass αᵐᵒᵖ R M] [IsCentralScalar α M] :
    IsCentralScalar α (Submodule R M) :=
  ⟨fun _a S => (congr_arg fun f : Module.End R M => S.map f) <| LinearMap.ext <| op_smul_eq_smul _⟩

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