P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929643863408640 |
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| author | Frisch, Sophie Halter-Koch, Franz |
| author_facet | Frisch, Sophie Halter-Koch, Franz |
| contents | 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). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_16350 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials Frisch, Sophie Halter-Koch, Franz Number Theory Commutative Algebra 11R32, 13F20, 20G30 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). |
| title | P-adic approximation of algebraic integers and residue class rings of rings of integer-valued polynomials |
| topic | Number Theory Commutative Algebra 11R32, 13F20, 20G30 |
| url | https://arxiv.org/abs/2412.16350 |