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Independence of Vector Space Axioms

  1. Jan 5, 2012 #1


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    1. The problem statement, all variables and given/known data

    Determine whether the commutativity of (V,+) is independent from the remaining vector space axioms.

    2. Relevant equations


    3. The attempt at a solution

    I am having a really hard time with this problem. Off the top of my head I could not think of any way to prove commutativity using the other axioms. On the other hand, I cannot think of any non-abelian groups (V,+) with a map R x V -> V that satisfies all the desired properties.

    If someone could get me pointed in the right direction, it would be appreciated.

    Edit: I should clarify that the underlying field is R
  2. jcsd
  3. Jan 5, 2012 #2


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    What can you deduce from

    [tex]2\cdot (x+y)=2\cdot x+2\cdot y[/tex]

    which is one of the axioms.
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