# Modules

• Feb 2nd 2009, 06:25 AM
peteryellow
Modules
Let R be a ring. prove that if M is a free R-module, then Ann_R M =0.
• Feb 2nd 2009, 05:17 PM
NonCommAlg
Quote:

Originally Posted by peteryellow

Let R be a ring. prove that if M is a free R-module, then Ann_R M =0.

let $r \in \text{ann}_R M$ and choose $x \in M$ to be in a basis of $M.$ then $rx=0$ and thus $r=0.$