On structures of the ring of arithmetical functions: prime ideals and beyond
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915272068169728 |
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| author | Goswami, Amartya Kleyn, Danielle Porrill, Kerry |
| author_facet | Goswami, Amartya Kleyn, Danielle Porrill, Kerry |
| contents | The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We also give an example of a semi-prime ideal that is not prime. We show that the ring of arithmetical functions has infinite Krull dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10824 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On structures of the ring of arithmetical functions: prime ideals and beyond Goswami, Amartya Kleyn, Danielle Porrill, Kerry Rings and Algebras 11A25, 11N64, 11R44 The aim of these notes is to study some of the structural aspects of the ring of arithmetical functions. We prove that this ring is neither Noetherian nor Artinian. Furthermore, we construct various types of prime ideals. We also give an example of a semi-prime ideal that is not prime. We show that the ring of arithmetical functions has infinite Krull dimension. |
| title | On structures of the ring of arithmetical functions: prime ideals and beyond |
| topic | Rings and Algebras 11A25, 11N64, 11R44 |
| url | https://arxiv.org/abs/2410.10824 |