Definition of "a field L algebraic over a field F"

Question

My book doesn't seem to give the definition of "a field L is algebraic over a field F ".

So I am guessing the definition of "L is algebraic over F"...

In the study of field extensions, does " field L is algebraic over a field F " mean the same thing as "L is an algebraic extension of F"?

Thank you!

Answer 1

Yep! Saying that [something] about $L$ happens "over" $F$ is another way to say that [something] is true about the extension $L/F$.