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- W209432704 abstract "Let K = Q( p mn; p dn; p d1m1n1') be an octic eld. If K is monogenic and a quadratic subeld Q( p d1m1n1) of K and a quartic subeld Q( p mn; p dn) are linearly disjoint, then K coincides with the eld Q( p 1; p 2; p 3); namely K is equal to the cyclotomic eld Q( 24) (MN). In this paper, we determine an explicit integral basis of an octic eld. Next, we prove that certain real octic elds K are non-monogenic slightly, but essentially generalizing the conditions in Theorem 0 (MN). K = Q( p mn; p dn; p d1m1n1'); where d = d1d2; m = m1m2; n = n1n2; mn 3; dn 2; d1m1n1' 1; d2 2 (mod 4); d1; m1; n1 1 and dmnl is square free. In this article, we consider the elds K whose Galois groups are 2-elementary abelian. Since K is non- monogenic for (K : Q) 16 and by the work (GT) of M.-N. Gras and F. Tano e, we may consider the case (K : Q) = 8 for d1m1n1' 1: Let k and L be a quadratic subeld Q( p d1m1n1) and a quartic subeld Q( p mn; p dn) of K; respectively. Then in the case" @default.
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- W209432704 date "2005-06-01" @default.
- W209432704 modified "2023-09-23" @default.
- W209432704 title "On Integral Bases of Certain Real Octic Abelian Fields" @default.
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