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