Journal of the Ramanujan Mathematical Society

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Euclidean Ideals in Quadratic Imaginary Fields


Affiliations
1 Queen’s University, Kingston, Ontario-K7L 3N6, Canada
2 DePaul University, Chicago, IL 60604, United States
     

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We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.
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  • Euclidean Ideals in Quadratic Imaginary Fields

Abstract Views: 234  |  PDF Views: 0

Authors

Hester Graves
Queen’s University, Kingston, Ontario-K7L 3N6, Canada
Nick Ramsey
DePaul University, Chicago, IL 60604, United States

Abstract


We classify all quadratic imaginary number fields that have a Euclidean ideal class. There are seven of them, they are of class number at most two, and in each case the unique class that generates the class-group is moreover norm-Euclidean.