implies that the minimal polynomial for over has degree 1. Hence the minimal polynomial is which implies .
I am reading Nicholson: Introduction to Abstract Algebra, Section 6.2 Algebraic Extensions.
Example 13 on page 282 (see attachment) reads as follows:
"If show that "
In the third line of the explanation - see page 282 of attachment - we read:
"But because ... ... "
Can someone explain why it follows that