I'm working on a problem from Dummit & Foote's Abstract Algebra and I can't figure out what exactly I'm being asked to prove. I hate to ask this here, because it seems that I should've been able to find an answer on my own. The problem is from Section 13.2 #19 and it reads:
Let $K$ be an extension of $F$ of degree $n$.
(a) For any $\alpha\in K$ prove that $\alpha$ acting by left multiplication on $K$ is an $F$-linear transformation of $K$.
I have searched and searched through the text and around on the internet and I cannot find an explicit definition of an "$F$-linear transformation". What does this mean?
If there is a definition for this in the book (or on the net) could anyone direct me to it?