Generators on exterior algebra in Flanders' Differential Forms text

Question

What does Harley Flanders mean when he states that f is defined on the generators of $\Lambda ^p \textbf(L)$? What are the generators?enter image description here

Answer 1

No, he doesn't mean a basis. The generators of $\Lambda^p L$ are the so-called primitive $p$-vectors, i.e., the wedge products of any $p$ vectors (which are interesting only when these $p$ vectors are linearly independent). Any $p$-vector is a linear combination of these, but they need not be linearly independent.