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        Primitive elements of abelian extensions and fields generated by polygon diagonals

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        ReinTerRele Bachelor Scriptie Versie 2 20-6.pdf (357.4Kb)
        Publication date
        2024
        Author
        Rele, Rein Ter
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        Summary
        In this thesis we are interested in primitive elements of abelian extensions of Q. By the Kronecker-Weber Theorem we know that abelian extensions are subfields of cyclotomic extensions Q(ζ_n). For the case where n = p^a with p an odd prime, we will show that the primitive elements of these field extensions are traces of powers of ζ_n over a subgroup H of the Galois group. In the last part of this thesis, we will discuss field extensions that are generated by the ratio of the lengths of two diagonals of a regular polygon. More specifically, we will discuss an article concerning this subject and show that there are some false claims in the article.
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        https://studenttheses.uu.nl/handle/20.500.12932/46764
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