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Unformatted text preview: (c) Is F isomorphic to a subeld of R ? Prove or disprove. (5) Let a 1 ,a 2 C be any two numbers which are algebraic over Q . Show that if there exists an isomorphism : Q ( a 1 ) Q ( a 2 ), leaving Q elementwise xed and satisfying ( a 1 ) = a 2 , then a 1 and a 2 have the same minimal polynomial over Q . (6) Fix a eld F , and dene a category C F whose objects are the extension elds of F . Dene morphisms in C F in such a fashion that the algebraic closure F of F arises as the solution of a universal mapping problem. Carefully formulate this problem and prove all of your claims....
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This note was uploaded on 03/11/2012 for the course MTHSC 851 taught by Professor Staff during the Fall '08 term at Clemson.
 Fall '08
 Staff
 Algebra

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