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Module action sends zero to zero?

  1. Dec 1, 2008 #1
    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..
     
  2. jcsd
  3. Dec 1, 2008 #2
    It's true:

    r0 = r(0 + 0) = r0 + r0. Canceling r0 from both sides gives 0 = r0.
     
  4. Dec 1, 2008 #3
    Oh, yes.. :shy:

    Thanks a lot!
     
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