Abstract
A general theorem on independency in a ℤ[G]-module is proved where G is a finite cyclic group. If applied to radical algebraic extensions of algebraic number fields, it yields a criterion of independency for systems of (parametric) units which contains as special cases theorems by Frei and Levesque and Halter-Koch and Stender.
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References
Frei, Günther and Levesque, Claude: On an Independent System of Units in the Field\(K = \mathbb{Q}(\sqrt[n]{{D^n \pm d}})\) where d|Dn, Abh. Math. Sem. Univ. Hamburg 50 (1980), 162–165
Frei, Günther and Levesque, Claude: Independent systems of units in certain algebraic number fields, J. reine angew. Math. 311/312 (1979), 116–144
Halter-Koch, Franz and Stender, Hans-Joachim: Unabhängige Einheiten für die Körper\(K = \mathbb{Q}(\sqrt[n]{{D^n \pm d}})\) mit d|Dn, Abh. Math. Sem. Univ. Hamburg 42 (1974), 33–40
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Frei, G. On the construction of independent units in cyclic or radical extensions. Manuscripta Math 61, 163–181 (1988). https://doi.org/10.1007/BF01259326
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DOI: https://doi.org/10.1007/BF01259326