Reduced ideals from the reduction algorithm

2017/11/20 by Tran, Ha Thanh Nguyen
#11H06 #11R11 #11Y40 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1711.07573

Abstract

The reduction algorithm is used to compute 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, we represent a sufficient and necessary condition for reduced ideals of real quadratic fields to be obtained from the reduction algorithm.

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