Module action sends zero to zero?

[geor]

Hello,

Excuse me if I ask something obvious here, but I can't
prove it..

Say R is a ring and M an R-module.
So, 0 \in M as M is an abelian group.

I guess r0=0, no?!

Can you tell me how we prove that?

Again, sorry if I ask something obvious..

 

[adriank]

It's true:

r0 = r(0 + 0) = r0 + r0. Canceling r0 from both sides gives 0 = r0.

 

[geor]

It's true:

r0 = r(0 + 0) = r0 + r0. Canceling r0 from both sides gives 0 = r0.

Oh, yes.. :shy:

Thanks a lot!