Abstract
The main goal of this paper is to calculate the index of any number field K generated by a root of an irreducible trinomial x 4 + a x + b ∈ Z [ x ] . Our approach is based on Engstrom’s results and the factorization of 2 Z K and 3 Z K . In particular, we reformulate the Davis and Spearman’s results. Namely, for every prime integer p, we evaluate ν p ( i ( K ) ) . The existence of a common index divisor of K guaranties the non monogenity of K.
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