Think minimal polynomials.
Example 13 from Nicholson: Introduction to Abstract Algebra, Section 6.2, page 282 reads as follows: (see attachment)
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Example 13: If show that
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The solution comes down to the following:
Given
so
Now Nicholson shows that and
so
Then Nicholson (I think) concludes that
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My problem is as follows:
How (exactly) does it follow that:
Can someone help?
Peter
Thanks SlipEternal ... well, given that the degree of minimal polynomial of the root u over is 1.
Thus I imagine the minimal polynomial is of the form x - u ... ... (the coefficients of the polynomial should be in ???)
How does this lead us to ?
I think I need a bit more help?
Peter
Sorry SlipEternal ... still not completely following.
Let me restate where I am (thanks to your help)
We have that the degree of the minimal polynomial m(u) of over is 1.
Thus, the minimal polynomial m(u) is a monic polynomial of degree 1 with coefficients in such that m(u) = 0.
So then where
How do we (formally) show that
Peter