Primordial element (algebra)

In algebra, a primordial element is a particular kind of a vector in a vector space. Let "V" be a vector space over a field "k" and fix a basis for "V" of vectors formula_1 for formula_2. By the definition of a basis, every vector "v" in "V" can be expressed uniquely as
Define formula_4, the set of indices for which the expression of "v" has a nonzero coefficient. Given a subspace "W" of "V", a nonzero vector "w" in "W" is said to be "primordial" if it has the following two properties: