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On the base of a relative number field, with an application to the composition of fields

1910
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Transactions of the American Mathematical Society
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It is a well known fact that in an algebraic number-field of degree n there exist n integers a" ■ • •, an such that every integer of the field can be expressed in the form where xx, x2, x3, ■ ■ -, xv ave rational integers. If we now consider a field relative to a given subfield of this field, from the nature of the proof of the above fact it is evident that, if the subfield in question is such that the number of classes of ideals in this field is one, and r the degree of the larger field

doi:10.1090/s0002-9947-1910-1500875-6
fatcat:gucgtydryralpkvv4qb6kxfpry