On the discriminant of some sextic elds

The computation of the discriminant of an algebraic number eld is a long-standing problem that has beenstudied by many authors. Here we deal with the discriminant of the algebraic number eld K = Q(θ)such that θ is a root of an irreducible trinomial g(X) = X۶ + b with integer coe cients, and such that theinteger b is not divisible by the ۶-th power of any prime. It is observed that for each prime number p, thehighest power of p dividing the discriminant of K is obtained in terms of the prime powers dividing b anddiscriminant of g(X). Let us rst recall some basic notions (see [۱]).

کلیدواژه ها:

Sextic elds ، discriminants of algebraic number elds ، rings of algebraic integers