Linear independence in a module
= Linear independence in a module
{title2=$\sum_i a_im_i=0\Longrightarrow a_i=0$}
Elements of a <module> are linearly independent if every finite linear relation between them has all coefficients zero. An independent finite set freely generates its span, a <finite free module>. Over an <integral domain>, maximal independence within a finite generating set enables <clearing denominators relative to an independent module subset>.