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1. CMB 2002 (vol 45 pp. 138)
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The Discriminant of a Dihedral Quintic Field Defined by a Trinomial $X^5 + aX + b$ Let $X^5 + aX + b \in Z[X]$ have Galois group $D_5$. Let $\theta$ be
a root of $X^5 + aX + b$. An explicit formula is given for the
discriminant of $Q(\theta)$.
Keywords:dihedral quintic field, trinomial, discriminant Categories:11R21, 11R29 |
2. CMB 1998 (vol 41 pp. 158)
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Power integral bases in composits of number fields In the present paper we consider the problem of finding power
integral bases in number fields which are composits of two
subfields with coprime discriminants. Especially, we consider
imaginary quadratic extensions of totally real cyclic number
fields of prime degree. As an example we solve the index form
equation completely in a two parametric family of fields of degree
$10$ of this type.
Categories:11D57, 11R21 |