Definition:Vector Space/Definition 1

Definition
Let $\struct {K, +_K, \times_K}$ be a division ring.

Let $\struct {G, +_G}$ be an abelian group.

Let $\struct {G, +_G, \circ}_K$ be a vector space over $K$.

If $\times_K$ is commutative, then $\struct {K, +_K, \times_K}$ is by definition a field.

In that case, the scalar ring of $\struct {G, +_G, \circ}_K$ is called the scalar field of $\struct {G, +_G, \circ}_K$.

Some sources insist that $\struct {K, +_K, \times_K}$ needs to be a field, not just a division ring, for this definition to be valid.