On Ring Class Fields of Number Rings

Hairong Yi; Chang Lv

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arXiv · 1810.04810

On Ring Class Fields of Number Rings

Hairong Yi·Chang Lv

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Abstract

For a number field $K$, we extend the notion of the ring class field of an order in $K$ [C. Lv and Y. Deng, SciChina. Math., 2015] to that of an arbitrary number ring in $K$. We give both ideal-theoretic and idele-theoretic description of this number ring class field, and characterize it as a subfield of the ring class field of some order. As an application, we use it to give a criterion of the solvability of a higher degree norm form equation over a number ring and finally describe algorithms to compute this field.

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Hairong Yi, Chang Lv. 2018-10-11. On Ring Class Fields of Number Rings. https://arxiv.org/abs/1810.04810

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