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Definition of a Module

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    I am curious if all modules contain 0.

    2. Relevant equations

    A left R-module M over the ring R consists of an abelian group (M, +) and an operation R × M → M such that certain properties hold...

    3. The attempt at a solution
    The definition of a module says that it is an additive group, and additive groups have the zero element. Thus, all modules contain the zero element right?



    Thank you.
     
  2. jcsd
  3. Oct 17, 2012 #2

    Dick

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    If 'zero' means the additive identity of the group, sure.
     
    Last edited: Oct 17, 2012
  4. Oct 17, 2012 #3

    HallsofIvy

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    Note that the ring, R, also has a "0" (additive identity) which is not necessarily the additive identity of M.
     
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