Cm Fields Without Unit-Primitive Elements

Abstract

This is an addendum to a recent paper by Zaïmi, Bertin and Aljouiee [‘On number fields without a unit primitive element’, Bull. Aust. Math. Soc.93 (2016), 420–432], giving the answer to a question asked in that paper, together with some historical connections.

CM fields with a reciprocal unit-primitive element

“…Several authors studied the question, initiated by Lalande, in [5], of whether a number field admits a reciprocal unitprimitive element (see, for instance, [4], [7], [8] and the references therein). An algebraic number ϑ is said to be reciprocal if 1/ϑ is a conjugate of ϑ .…”