Abstract
ABSTRACT Let K be a number field generated by a root θ of a monic irreducible trinomial F ( x ) = x n + a x m + b ∈ ℤ [ x ] . In this paper, we study the problem of monogenity of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic. As applications, we show that there are infinite families of non-monogenic number fields defined by trinomials of degree n = 2 r · 3 k with r and k two positive integers. We also give infinite families of non-monogenic sextic number fields defined by trinomials. Some illustrating examples are giving at the end of this paper.
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