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Totally positive units and squares

Authors: I. Hughes and R. Mollin
Journal: Proc. Amer. Math. Soc. 87 (1983), 613-616
MSC: Primary 12A45; Secondary 12A35, 12A95
MathSciNet review: 687627
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Abstract: Let $ K$ be a finite cyclic extension of the rational number field $ Q$, with Galois group $ G(K/Q)$ of order $ {p^a}$ for an odd prime $ p$. Armitage and Fröhlich [1] proved that if the order of 2 modulo $ p$ is even and the class number $ {h_K}$ of $ K$ is odd then $ U_K^ + = U_K^2$, where $ {U_K}$ is the group of units of the ring of integers $ {\mathcal{C}_K}$ of $ K$, $ U_K^ + $ is the group of totally positive units, and $ U_K^2$ is the group of unit squares. The purpose of this paper is to provide a generalization of this result to a larger class of abelian extensions of $ {Q.^2}$

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Keywords: Totally positive units, squares, cyclotomic units, class field theory
Article copyright: © Copyright 1983 American Mathematical Society

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