How one determines the degree of an element in the exterior algebra $\bigwedge V$, for a graded vector space V.

e.g.Is it true that $\wedge^n V^2=0$, as elements of $V^2$ are of degree 2?

In particular, when does the exterior product vanish? Thanks!

  • $\begingroup$ I do not understand the notation, what does $V^2$ mean? $\endgroup$ – Siddharth Bhat Jul 10 at 12:09
  • $\begingroup$ as $V$ is graded $V=V^0\oplus V^1\oplus V^2\oplus..$ $\endgroup$ – sasho98 Jul 10 at 12:10

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