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 dK.
Battistoni, F., Discriminants of number fields and surjectivity of tracehomomorphism on rings of integers, <<RENDICONTI DEL SEMINARIO MATEMATICO>>, 2020; 78 (1): 13-19 [https://hdl.handle.net/10807/270255]
Discriminants of number fields and surjectivity of trace homomorphism on rings of integers
Battistoni, Francesco
2020
Abstract
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 dK.
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