# Name for binary operation between two sets

If $$\mathsf{X}$$ is a set, a binary operation on it is a map $$*:\mathsf{X}\times\mathsf{X}\to\mathsf{X}$$. Examples of these operations are addition and multiplication in a field.

The scalar multiplication in a vector space $$\mathsf{V}$$ over a field $$\mathsf{F}$$ is defined as a map $$\cdot:\mathsf{F}\times\mathsf{V}\to\mathsf{V}$$. This doesn't fit into the definition of a binary operation unless $$\mathsf{V}=\mathsf{F}$$. What is it called? Is there a term for it?

• Aaah found it! It's called a left external binary operation on $\mathsf{V}$ over $\mathsf{F}$! May 27 at 14:20
• The answer provided below is much more common. May 27 at 14:31

• $$F$$ acts on $$V$$
• An action of $$F$$ on $$V$$