Some remarks on the ring of arithmetical functions
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866910615339008000 |
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| author | Goswami, Amartya |
| author_facet | Goswami, Amartya |
| 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 show arithmetic ring has infinite Krull dimension and its associated prime ideal set is nonempty. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_01072 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Some remarks on the ring of arithmetical functions Goswami, Amartya Rings and Algebras 11A25, 13F25 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 show arithmetic ring has infinite Krull dimension and its associated prime ideal set is nonempty. |
| title | Some remarks on the ring of arithmetical functions |
| topic | Rings and Algebras 11A25, 13F25 |
| url | https://arxiv.org/abs/2302.01072 |