Independence of Vector Space Axioms

  • Thread starter jgens
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jgens
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Homework Statement



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

Homework Equations



N/A

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
 

Answers and Replies

  • #2
22,089
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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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