Power Integral basis in Algebraic Number Fields whose Galois Groups are 2-Elementery Abelian

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تک‐سرشتی میدان های عددی با گروه گالوای 2‐ابتدایی

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 50858 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Pournaki, Mohammad Reza; Rajaei, Ali
Abstract:
LetK be a biquadratic field. M.-N. Gras and F. Tanoe gave a necessary and sufficient condition that K is monogenic by using a diophantine equation of degree 4 [13]. We consider algebraic extension fields of higher degree. Let F be a Galois extension field over the rationals Q whose Galois group is 2-elementary Abelian. then we shall prove that F of degree graeter than 8, is monogenic if and only if F being field of n'th primitive root of unity under a suitable condition for the case of degree 8
Keywords:
Monogenic ; Power Integral Basis ; HASSE Problem