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The Fundamental Unit of Some Quadratic, Cubic or Quartic Orders
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We explain why it is reasonable to conjecture that if ∈ is a totally imaginary quartic unit, then ∈ is in general a fundamental unit of the quartic order Z[∈], order whose group of units is of rank equal to one. We partially prove this conjecture. This generalizes a result of T. Nagell, who proved in 1930 a similar result for real cubic units with two non real conjugates.
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