Is the set of integers a vector space?

My friend says it's not, because he thinks vectors have to have have at least two elements, otherwise they're scalars. I say that (Z, +, *) satisfies the axioms of a vector space and that's all you need.

What does /sci/ think?

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>>15

Okay, so if I'm understanding correctly: Z is not a vector space because it's not over a field, and that's because not all (in fact, only two) of its elements have multiplicative inverses. Right?