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Power Bases in Dihedral Quartic Fields

✍ Scribed by Anthony C Kable

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
119 KB
Volume
76
Category
Article
ISSN
0022-314X

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✦ Synopsis

A quartic number field, L, is called dihedral if the normal closure, N, of L satisfies Gal(NΓ‚Q)$D 8 . We investigate whether or not the ring of integers of such a quartic field has a power basis. When the quadratic subfield of L is imaginary, the problem is completely solved. When it is real, the same method leads to a solution in many cases. Several numerical illustrations of the method are given.

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