Proving n is a multiple of the ring characteristic

[jmjlt88]

I was looking back at a proof I did a while ago. Suppose na=0 with n≠0 and a≠0. Then n is a multiple of the characteristic. I supposed p < n is our characteristic, then I simply used the divison algorithm (I divided n by p) and the distributive property which lead to the remainder being 0. From there, I concluded the desired result. I don't want to bore anyone with the details, but does that seem like a valid approach.

Thanks! :shy:

 

[micromass]

Seems ok!