Lemma 10.13.1. Let $R$ be a ring. Let $M$ be an $R$-module. If $M$ is a free $R$-module, so is each symmetric and exterior power.

Proof. Omitted, but see above for the finite free case. $\square$

There are also:

• 2 comment(s) on Section 10.13: Tensor algebra

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).