Abstract
The reduction algorithm is used to compute the reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among reduced ones. Especially, for some number fields, we present the conditions of the reduced ideals produced by the reduction algorithm. Additionally, our results partly answer the question by R. Schoof who asks about the number of the reduced ideals that can not be produced by the reduction algorithm.
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Acknowledgements
Peng Tian is supported by NSFC (NOs: 11601153) and Ha T. N. Tran was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) (funding RGPIN-2019-04209 and DGECR-2019-00428).
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Tian, P., Tran, H.T.N. Reduced Ideals from the Reduction Algorithm. Results Math 79, 50 (2024). https://doi.org/10.1007/s00025-023-02076-1
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DOI: https://doi.org/10.1007/s00025-023-02076-1