In algebra I'm having trouble with this definition:(adsbygoogle = window.adsbygoogle || []).push({});

The extensions K of F is a simple extension of F if F = F(a) for some a in K.

What I understand so far:

F is a set. But the notation F(a) has me lost-- what is it? Is is the values you get when you plug a in to any polynomial over th field F? So, one value in the set F(a) would be:

[tex]b_{1}(a)+b_{2}(a)^{3}+b_{3}(a)^{9}+b_{4}[/tex]

Where the bi are from F ? And I can make any polynomial like that then fin it's value for a?

This is hard to think about.

Also... is the meaning for F(a,b) ... that I can plug in a or b? or can I mix and match like this:

[tex]c_{1}(a)-c_{2}(b)^{5}+c_{3}(b)^{9}+c_{4}[/tex]

Is that in F(a, b)... or is it just stuff like:

[tex]c_{1}(a)+c_{2}(a)^{5}-c_{3}(a)^{9}+c_{4}[/tex]

[tex]c_{1}(b)+c_{2}(b)^{5}+c_{3}(b)^{9}+c_{4}(b)^{9}+c_{5}[/tex]

with the ci in F.

Help!

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# Homework Help: In algebra I'm having trouble with this definition: simple extension

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