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Algebraic Numbers and Fields are investigated. The solution is detailed and well presented.
Algebraic Numbers - Show that there are infinitely many algebraic numbers such that . If and are distinct algebraic numbers with = , then what are the possible values of ? Illustrate each value in your list by givin ...
Fields, Transcendence Basis and Algebraic Dependence - CORRECTION: In this problem, transcendence degree should *add*, not multiply as the prblem states.
Also, that last letter in the problem that is cut-off is "L".
Please see the attached file fo ...
Extension of fields - Let K/F be an extension of fields. Let a be an element of K such that a^2 is algebraic over F. Prove that a is also algebraic over F.
Fields Extensions/Algebraic - Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K ...