Is Z2xZ2 even a vector space?

[hasty schooner]

With the base field Z.
The element (1,0) * 2 =(2,0)=(0,0) doesn't this prove that it isn't a vector space?

[lavish spoke]

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[rain pendant]

It's a vector space over the field $\mathbb{Z}/2$. $\mathbb{Z}$ is not a field so there cannot be any vector spaces over it. Instead, it is a module over $\mathbb{Z}$. Modules are analogous to vector spaces for communicative rings like $\mathbb{Z}$.

[olive crow]

mark4slr

[hasty schooner]

+close