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arXiv · 2412.16350

P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials

Sophie Frisch·Franz Halter-Koch
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Abstract

Let F:K be a Galois extension of number fields and Q a prime ideal of O_F lying over the prime P of O_K. By analyzing the Q-adic closure of O_K in O_F we characterize those rings of integers O_K for which every residue class ring of Int(O_K) modulo a non-zero prime ideal is GE2 (meaning that every unimodular pair can be trasformed to (1,0) by a series of elementary transformations).

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Sophie Frisch, Franz Halter-Koch. 2024-12-20. P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials. https://arxiv.org/abs/2412.16350

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