 
Summary: An integral basis and the discriminant
of a quintic field defined by a
trinomial x5
+ ax + b
Ay¸se Alaca and S¸aban Alaca
ABSTRACT. Let K = Q() be a quintic field, where is a root of an irreducible
trinomial x5 + ax + b, a, b Z. We determine a pintegral basis of K for each
prime p. Then we obtain an integral basis of K from its pintegral bases, and we
give an explicit formula for the discriminant of K.
1 Introduction
In this paper we determine, for each prime p, a pintegral basis for a quintic
field K = Q(), where is a root of an irreducible trinomial
x5
+ ax + b, a, b Z.
Then we obtain an integral basis of K from its pintegral bases, and give an
explicit formula for the discriminant of K.
Llorente, Nart and Vila [3] determined the discriminant of a number
field defined by an irreducible trinomial
xn
+ axs
