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Bounding a unit index in terms of a ring index

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  26 February 2010

John Wolfskill
John Wolfskill
Affiliation:
Department of Mathematics, Northern Illinois University, DeKalb, IL 60115, U.S.A.
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Abstract

Let R⊂S be two orders in a number field, and let ER and ES be the respective groups of units in each ring. Then ES/ER and S/R are both finite. We consider the problem of bounding the order of ES/ER in terms of the index of R in S. In this paper we solve this problem in the special case that S/R is cyclic as a module over Z.

MSC classification

Secondary: 11R27: Units and factorization
Type
Research Article
Information
Mathematika , Volume 42 , Issue 1 , June 1995 , pp. 199 - 205
Copyright
Copyright © University College London 1995

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References

1. Cohn, H.. A classical invitation to algebraic numbers and class fields (Springer-Verlag, New York, 1978).Google Scholar