Let be fields such that . Prove that if is a basis for over and is a basis for over , then is a basis for over . Conclude that if and are finite, then .
I know how to do the proof, but I'm not sure how to conclude that . Some help please.
Let be fields such that . Prove that if is a basis for over and is a basis for over , then is a basis for over . Conclude that if and are finite, then .
I know how to do the proof, but I'm not sure how to conclude that . Some help please.