Discriminants of number fields and surjectivty of trace homomorphism on rings of integers

Francesco Battistoni

Published 2019-10-25Version 1

In this note we give a brief survey of the most elementary criteria used to determine the surjectivity of the trace operator on the ring of integers of a number field $K$. Furthermore, we introduce an easy to state yet unknown surjectivity criterion depending only on the prime factorization of the degree $n$ of $K$ and on the squarefree part of the discriminant $d_K$.