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I am reading Anderson and Feil - A First Course in Abstract Algebra.

I am currently focused on Ch. 45: The Splitting Field ... ...

I need some help with an aspect of the proof of Theorem 45.6 ...

Theorem 45.6 and its proof read as follows:

At the start of the proof of Theorem 45.6 we read the following:

"Suppose that ##K## is a normal extension of ##F##, a field with characteristic zero. Then by Theorem 45.5, ##K = F( \alpha )##, where ##\alpha## is algebraic over ##F##. ... .. "

The quote mentions Anderson and Feil's Theorem 45.5 and also mentions that K is a normal extension so I am providing the statement of Theorem 45.5 and Anderson and Feil's definition of a normal extension as follows ... ...

Hope someone can help ...

Peter

I am currently focused on Ch. 45: The Splitting Field ... ...

I need some help with an aspect of the proof of Theorem 45.6 ...

Theorem 45.6 and its proof read as follows:

At the start of the proof of Theorem 45.6 we read the following:

"Suppose that ##K## is a normal extension of ##F##, a field with characteristic zero. Then by Theorem 45.5, ##K = F( \alpha )##, where ##\alpha## is algebraic over ##F##. ... .. "

**Can someone please explain**__exactly__how ##K = F( \alpha )## follows in the above statement ... ?The quote mentions Anderson and Feil's Theorem 45.5 and also mentions that K is a normal extension so I am providing the statement of Theorem 45.5 and Anderson and Feil's definition of a normal extension as follows ... ...

Hope someone can help ...

Peter