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Can there be noncommutative vector space? Vecor space with addition forms abelian group, can there exist similar object which forms nonabelian group under addition? If so, how are these object called, are they being studied, where can I find something about them
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>>9067646
You can look at modules over noncommutative rings, where scalar multiplication would be noncommutative.
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>>9067659
I'm not asking about modules but about structure similar to vector space over a field where vector addition is not commutative
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>>9067646
https://en.wikipedia.org/wiki/Group_with_operators
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Not if you keep all other axioms, see
http://planetmath.org/definitionofvectorspaceneedsnocommutativity
Now you could invest some time and think about which axioms to drop.
I'd be interested to see what happens when you drop
(a+b)· v = a · v + b · v
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