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Is it possible to construct a quasi-vectorial space without an identity element?

I know that the commutativity of vector addition is a consequence of the others conditions in the definition of a vector space. I do not think that the associativity of vector addition is a consequence of the others conditions (I am including the commutativity among them). How do I prove that? In fact, I do not even know what I should do.

I would appreciate any help.

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    Commutativity only follows form the other axioms if the additive inverse axiom (equivalently, the cancellation axiom) is stated as holding *on both sides*. In most axiomatizations of vector spaces that I am familiar with in which the axioms of vector addition are stated explicitly (as opposed to simply saying "$(V,+)$ is an abelian group"), this is **not** the case: both the additive identity and additive inverse axioms are stated on a single side; if you do *that*, then commutative does *not* follow from the other axioms, as shown in the examples given in the post refered to above.2012-01-29

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