A Family of Number Fields with Unit Rank at Least 4 That Has Euclidean Ideals
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چکیده
We will prove that if the unit rank of a number field with cyclic class group is large enough and if the Galois group of its Hilbert class field over Q is abelian, then every generator of its class group is a Euclidean ideal class. We use this to prove the existence of a non-principal Euclidean ideal class that is not norm-Euclidean by showing that Q( √ 5, √ 21, √ 22) has such an ideal class.
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تاریخ انتشار 2013