Factorization of Lipschitzian Elements

A lipschitzian element a is given in a Clifford algebra C?(V, q) over a field K that contains at least three scalars. Here we prove that, if a is not in the subalgebra generated by a totally isotropic subspace of V, then it is a product of linearly independent vectors of V. An effective algorithm is proposed to decompose a into such a product of vectors.