mkQ — Mathlib

English

The quotient M/P has a SMulZeroClass structure compatible with mk, ensuring a • 0 = 0.

Русский

Фактор-модуль M/P имеет структуру SMulZeroClass, совместимую с mk: a • 0 = 0.

LaTeX

$$$\forall a \in S,\ a \cdot 0_{M/P} = 0_{M/P}$$$

Lean4

/-- The map from a module `M` to the quotient of `M` by a submodule `p` as a linear map. -/
def mkQ : M →ₗ[R] M ⧸ p where
  toFun := Quotient.mk
  map_add' := by simp
  map_smul' := by simp

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