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?
Best Answer
"Action" or more generally a "left-action"
Examples: