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Unformatted text preview: Q [ x ] is a UFD. Let r = f / g Q ( x ) (the eld of fractions of Q [ x ] ) with f , g Q [ x ] \ 0, coprime (no common irreducible factor), and at least one of f , g has degree nonzero. (a) Prove that there is a unique monomorphism r : Q ( x ) Q ( x ) such that r ( x ) = r . (b) If f and g both have degree at most 1, prove that r is an automorphism. Hint: if r = ax + b cx + d , consider the inverse of the matrix a b c d and use this to construct s Q ( x ) such that r s ( x ) = s r ( x ) = x . (4 points) 5. Section 8.3, Exercise 2 on page 293. (2 points) (5 problems, 13 points altogether)...
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This note was uploaded on 01/02/2012 for the course MATH 5125 taught by Professor Palinnell during the Fall '07 term at Virginia Tech.
 Fall '07
 PALinnell
 Math, Algebra

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