How one can define right vector space over Division ring $R$ ? What properties it lack than the vector space over field? One thing which it lack is definitely commutative properties but what other properties it lacks?
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2Not much is lost: everything about dimension an bases carries over. Inner products cannot be used and the dual of a right vector space is a left vector space. – egreg Mar 07 '19 at 08:02
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2Does everyone get to see the same 'Related' questions in the side bar, or is this 'personalized' dependent on all sort of creepy tracking cookies in your browser? Anyway, the top suggestion in my side bar, https://math.stackexchange.com/q/45056/101420 seems to have a lot of useful answers to your question – Vincent Mar 07 '19 at 08:14
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@Vincent Everyone sees related questions, which, I should think is likely, is only based on the question you are viewing, no cookies or anything. It looks very similar to the list that appears when you author a question. What about it made you think it is personalized? – rschwieb Mar 07 '19 at 16:09
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@maths . "One thing which it lack is definitely commutative properties" Do you mean that an expression like $\lambda v=v\lambda$ for $\lambda \in D$ and $v\in V$ doesn't hold? Yes indeed. In fact, given no other information, "$\lambda v$" doesn't even have any meaning in a "right vector space." – rschwieb Mar 07 '19 at 16:11