An analogue of Rogers' theorem on sieving in commutative rings
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909011104759808 |
|---|---|
| author | Kucheriaviy, Petr |
| author_facet | Kucheriaviy, Petr |
| contents | We prove that an analogue of Rogers' theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14080 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An analogue of Rogers' theorem on sieving in commutative rings Kucheriaviy, Petr Commutative Algebra Number Theory We prove that an analogue of Rogers' theorem on sieving holds for an order if and only if the order is a Dedekind domain. We also prove that it holds for a finite commutative ring if and only if the ring is a direct product of local rings with linearly ordered ideals. |
| title | An analogue of Rogers' theorem on sieving in commutative rings |
| topic | Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2603.14080 |