Correct the definition of the italicized term without reference to the text, if correction is needed, so that it is in a form acceptable for publication.

A basis for a nonzero abelian group G is a generating set X ⊆ G such that n₁x₁ + n₂x₂ + · · · + n_mX_m = 0 for distinct x_i ∈ X and n_i ∈ Z only if n₁ = n₂ =···= n_m= 0.