JP Journal of Algebra, Number Theory and Applications
Volume 4, Issue 2, Pages 261 - 299
(August 2004)
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AN
INTEGRAL BASIS AND THE DISCRIMINANT OF A QUINTIC
FIELD DEFINED BY A TRINOMIAL x5
+ ax + b
Ayse Alaca (Canada) and Şaban Alaca (Canada)
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Abstract: Let
K
= Q(q)
be a quintic field, where q
is a root of an irreducible trinomial X5
+ ax + b, a, b Î
Z.
We determine a p-integral basis of K for
each prime p. Then we obtain an integral
basis of K from its p-integral
bases, and we give an explicit formula for the
discriminant of K. |
Keywords and phrases: quintic field, trinomial,
p-integral basis, integral basis, discriminant. |
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