distribSMul — Mathlib

English

The quotient M/P satisfies DistribSMul with the scalars acting on the quotient in the natural way: a • [x] distributes over addition.

Русский

Фактор-модуль M/P удовлетворяет DistribSMul: действие скаляра на фактор-модуль распределяет над сложением.

LaTeX

$$$\forall a \in S,\forall [x],[y] \in M/P,\ a \cdot ([x] + [y]) = a \cdot [x] + a \cdot [y]$$$

Lean4

instance distribSMul (P : Submodule R M) : DistribSMul R (M ⧸ P) :=
  Quotient.distribSMul' P

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