I need a rigourous proof for the following problem if possible:-
Let L be a finite extension of F and let K be a subfeild of L such that it contains F.
Show that [K:F] | [L:F] .
I need a rigourous proof for the following problem if possible:-
Let L be a finite extension of F and let K be a subfeild of L such that it contains F.
Show that [K:F] | [L:F] .
Please help.
If and is finite then and is finite. Furthermore, . Therefore, divides . To see this, note if is basis for and is basis for then is a basis for .