= Coordinate support in a free module
{title2=$\operatorname{supp}_E(m)=\{e\in E:r_e\ne0\}$}
= Coordinate supports in a free module
{synonym}
= Basis support
{synonym}
For an element $m=\sum_{e\in E}r_ee$ of a <free module> with specified <basis of a module> $E$, its coordinate support is the finite set of <basis of a module> elements having nonzero coefficients. This is well-defined by uniqueness of the expression. The coordinate support of a sum is contained in the union of the two coordinate supports, and scalar multiplication cannot enlarge it. It is distinct from the prime-ideal-valued <support of a module>.
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