A class of number fields without odd rational prime index divisors

‎In this work‎, ‎for every number field K generated by a root of a monic irreducible trinomial F(x) = x^{۷}‎ + ‎a.x^{۶}‎ + ‎b \in \mathbb{Z}[x]‎, ‎we show that no odd rational prime p divides the index i(K)‎, ‎and we give the necessary and sufficient conditions on a‎, ‎b such that ۲ divides i(K)‎. ‎Specifically‎, ‎we provide adequate requirements for K to be non-monogenic‎. ‎Finally‎, ‎several computational examples are used to illustrate our conclusions‎.

کلیدواژه ها:

Monogeneity ، Newton polygon ، prime ideal factorization ، Dedekind ، Common index divisor ، Theorem of Ore