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Let \(F:K\) be a Galois extension of number fields and Q a prime ideal of \({\mathcal {O}}_F\) lying over the prime P of \({\mathcal {O}}_K\) . By analyzing the Q-adic closure of \({\mathcal {O}}_K\) in \({\mathcal {O}}_F\) we characterize those rings of integers \({\mathcal {O}}_K\) for which every residue class ring of \({{\,\textrm{Int}\,}}({\mathcal {O}}_K)\) modulo a non-zero prime ideal is \({\textrm{GE}}_2\) (meaning that every unimodular pair can be transformed to (1, 0) by a series of elementary transformations).

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P-adic Approximation of Algebraic Integers and Residue Class Rings of Rings of Integer-Valued Polynomials

  • 会议论文

  • 发表日期：

    2025年

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  • Sophie Frisch,
  • Franz Halter-Koch

摘要

Let \(F:K\) be a Galois extension of number fields and Q a prime ideal of \({\mathcal {O}}_F\) lying over the prime P of \({\mathcal {O}}_K\) . By analyzing the Q-adic closure of \({\mathcal {O}}_K\) in \({\mathcal {O}}_F\) we characterize those rings of integers \({\mathcal {O}}_K\) for which every residue class ring of \({{\,\textrm{Int}\,}}({\mathcal {O}}_K)\) modulo a non-zero prime ideal is \({\textrm{GE}}_2\) (meaning that every unimodular pair can be transformed to (1, 0) by a series of elementary transformations).