not_linearIndependent_pair_of_flat_right

English

The not-linear-independence of a commuting pair in the flat-right case holds under linear disjointness.

Русский

Не линейная независимость пары, когда правая плоскость, сохраняется при линейной несовместности.

LaTeX

$$¬LinearIndependent R ![a,b]$$

Lean4

/-- The `Submodule.LinearDisjoint.not_linearIndependent_pair_of_commute_of_flat_right`
for commutative rings. -/
theorem not_linearIndependent_pair_of_flat_right [Module.Flat R N] (a b : ↥(M ⊓ N)) : ¬LinearIndependent R ![a, b] :=
  H.not_linearIndependent_pair_of_commute_of_flat_right a b (mul_comm _ _)

Похожие утверждения