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Greither, Cornelius and Zaïmi, Toufik 2018. CM fields with a reciprocal unit-primitive element. Comptes Rendus Mathematique, Vol. 356, Issue. 1, p. 8.
Zaïmi, Toufik 2017. A note on number fields having reciprocal integer generators. Quaestiones Mathematicae, Vol. 40, Issue. 3, p. 391.
We characterise number fields without a unit primitive element, and we exhibit some families of such fields with low degree. Also, we prove that a noncyclotomic totally complex number field 
$K$
, with degree 
$2d$
where 
$d$
is odd, and having a unit primitive element, can be generated by a reciprocal integer if and only if 
$K$
is not CM and the Galois group of the normal closure of 
$K$
is contained in the hyperoctahedral group 
$B_{d}$
.
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