instIsCentralScalar — Mathlib

English

Derivation(R,A,M) has an AddCommMonoid structure defined pointwise by addition and zero.

Русский

Derivation(R,A,M) имеет структуру AddCommMonoid, заданную по точкам сложением и нулем.

LaTeX

$$$D_1 + D_2 : \mathrm{Derivation}(R,A,M)$ and $0 : \mathrm{Derivation}(R,A,M)$ satisfy $(D_1 + D_2)(a) = D_1(a) + D_2(a)$ and $0(a) = 0$.$$

Lean4

instance [DistribMulAction Sᵐᵒᵖ M] [IsCentralScalar S M] : IsCentralScalar S (Derivation R A M) where
  op_smul_eq_smul _ _ := ext fun _ => op_smul_eq_smul _ _

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