Suppose I am handed a k-form $\omega$. What can I do to check if $\omega$ can be expressed in the form
$$\omega = \alpha_1 \wedge \dots \wedge \alpha_k?$$
The context for this question is an application in differential geometry. A codimension-k surface is characterized by a k-form field of the above form; I am trying to ascertain when a specified k-form field defines a codimension-k surface
EDIT: An equivalent question is, "when is a given k-form the unique top-level form of some k-dimensional subspace?"