Abstract
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.
| Original language | English |
|---|---|
| Article number | 2650243 |
| Journal | Journal of Algebra and its Applications |
| DOIs | |
| Publication status | Accepted/In press - 2025 |
Keywords
- Arithmetic functions
- Dirichlet convolutions
- Krull dimension
- local rings
- prime ideal
- unique factorization domains
ASJC Scopus subject areas
- Algebra and Number Theory
- Applied Mathematics
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University of Johannesburg Reports Findings in Algebra (Some Structural Aspects of the Ring of Arithmetical Functions: Prime Ideals and Beyond)
11/06/25
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