Algebraic integers on the unit circle (Q852528)

The author investigates which number fields contain units of modulus \(1\) that are not roots of unity. This question was treated by \textit{C. R. MacCluer} and \textit{C. J. Parry} [J. Number Theory 7, 371--375 (1975; Zbl 0319.12002)]. In this note, the author obtains slightly more general result. Furthermore, his proof is simpler. The main result of the paper asserts that a number field \(K\) contains unimodular units that are not roots of unity if and only if the field \(K \cap \overline{K}\) is imaginary and not a CM-field.