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December 4th, 2008, 12:56 AM
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| | algebraic extension proof I need help with this proof. Let E be an algebraic extension of field F. If R is a ring and F is contained in R is contained in F, show that R must be a field.
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December 4th, 2008, 01:19 AM
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Originally Posted by morganfor I need help with this proof. Let E be an algebraic extension of field F. If R is a ring and F is contained in R is contained in E, show that R must be a field.
Thanks! | let  and ![p(x)=x^n + a_1x^{n-1} + \cdots + a_{n-1}x+a_n \in F[x] p(x)=x^n + a_1x^{n-1} + \cdots + a_{n-1}x+a_n \in F[x]](http://www.mathhelpforum.com/math-help/latex2/img/fe94dbce536b412e8dfcb389340ebbaa-1.gif) be the minimal polynomial of  then  and thus: | | The following users thank NonCommAlg for this useful post: | |  | 
December 4th, 2008, 11:28 AM
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| | Thanks! I get it all the way up until the last part. How did you get the final polynomial and how is it that when you multiply it by r you get 1? | 
December 4th, 2008, 01:30 PM
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Originally Posted by morganfor Thanks! I get it all the way up until the last part. How did you get the final polynomial and how is it that when you multiply it by r you get 1? | By moving  over to the other side and dividing by  both sides. | | Thread Tools | | | | Display Modes | Linear Mode |
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