On Indices of Septic Number Fields Defined by Trinomials <i>x</i>⁷ + <i>ax</i> + <i>b</i>

Abstract

Let K be a septic number field generated by a root, α, of an irreducible trinomial, x7+ax+b∈Z[x]. In this paper, for every prime integer, p, we calculate νp(i(K)); the highest power of p dividing the index, i(K), of the number field, K. In particular, we calculate the index, i(K). In application, when the index of K is not trivial, then K is not monogenic.

Keywords

• power integral bases
• theorem of Ore
• prime ideal factorization
• common index divisor