Definition:Vector Space

Let $$\left({K, +_K, \times_K}\right)$$ be a division ring.

Let $$\left({G, +_G}\right)$$ be an abelian group.

Let $$\left({G, +_G: \circ}\right)_K$$ be a unitary $K$-module.

Then $$\left({G, +_G: \circ}\right)_K$$ is a vector space over $$K$$ or a $$K$$-vector space.

That is, a vector space is a unitary module whose scalar ring is a division ring.