The index of θ , where θ is a primitive element of some algebraic number Field

An algebraic number eld K is a nite extension of the eld of rational numbers Q. It can be generated bya single element. If K is of degree n = [K : Q], then there exists an algebraic number of degree n, suchthat K = Q(θ); so is a primitive element of such algebraic number eld. The ring of integers ZK of K isthe set of algebraic integer elements of K (having minimal polynomial with integers coe cients and leadingcoe cient ۱). If K = Q(θ) with an algebraic integer, the index [ZK : Z[θ]] is called the index of θ , anddenoted by Ind( ) (see [۳]).

کلیدواژه ها:

Algebraic number elds ، the index of an algebraic element