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Unformatted text preview: n ≥ 1. Solution. False. (ii) There are no 5th roots of unity in a f eld of characteristic 5. Solution. False. (iii) R is a splitting f eld of x 2 − 5 over Q . Solution. False. (iv) Q ( √ 5 ) is a normal extension of Q . Solution. False. (v) No polynomial of degree ≥ 5 in Q [ x ] is solvable by radicals. Solution. False. (vi) F 2 ( x ) = Frac ( F 2 [ x ] ) is an in f nite f eld of characteristic 2. Solution. True. (vii) A polynomial f ( x ) ∈ Q [ x ] can have two splitting f elds inside of C . Solution. False. (viii) The alternating group A 4 is a solvable group. Solution. True....
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This note was uploaded on 12/21/2011 for the course MAS 4301 taught by Professor Keithcornell during the Fall '11 term at UNF.
- Fall '11