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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Class groups, totally positive units, and squares


Authors: H. M. Edgar, R. A. Mollin and B. L. Peterson
Journal: Proc. Amer. Math. Soc. 98 (1986), 33-37
MSC: Primary 11R37; Secondary 11R27
MathSciNet review: 848870
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Abstract: Given a totally real algebraic number field $ K$, we investigate when totally positive units, $ U_K^ + $, are squares, $ U_K^2$. In particular, we prove that the rank of $ U_K^ + /U_K^2$ is bounded above by the minimum of (1) the $ 2$-rank of the narrow class group of $ K$ and (2) the rank of $ U_L^ + /U_L^2$ as $ L$ ranges over all (finite) totally real extension fields of $ K$. Several applications are also provided.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1986-0848870-X
PII: S 0002-9939(1986)0848870-X
Article copyright: © Copyright 1986 American Mathematical Society