I have troubles picturing what elements belong to a particular ensemble.
Let $\omega_1$,...,$\omega_r$ be differential 1-forms on a $C^\infty$ n-manifold that are independent at each point. Considering a complete base $\omega_1$,...,$\omega_r$,...,$\omega_{r+1}$,...,$\omega_{n}$, could someone give me some examples and counter-examples of elements in the ideal $\mathscr{I}$ generated by $\omega_1$,...,$\omega_r$ ?
For example, what to do with $\omega^1\wedge\omega^{r+2}$ ?
Thank you,
JD