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Topic: evaluation homomorphism
Replies: 5   Last Post: Mar 25, 2011 5:28 PM

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Posts: 12
Registered: 4/20/09
evaluation homomorphism
Posted: Mar 25, 2011 3:43 AM
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Hey mathematicians,

I'm looking at Fraleigh's First Course in Abstract Algebra book, 7th.

Theorem 22.4 states

Let F be a subfield of a field E, let alpha be any element of E, and let x
be an indeterminate. The map Psi_alpha: F[x] --> E defined by Psi_alpha(n
degree polynomial) = alpha plugged into the polynomial is a homomorphism.

I don't understand why this book keeps specifying that Psi_alpha(x) = alpha.
Isn't this obvious from just plugging in alpha for the indeterminate?


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