On structures of the ring of arithmetical functions: prime ideals and beyond
Rings and Algebras
2025-05-06 v2
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.
Keywords
Cite
@article{arxiv.2410.10824,
title = {On structures of the ring of arithmetical functions: prime ideals and beyond},
author = {Amartya Goswami and Danielle Kleyn and Kerry Porrill},
journal= {arXiv preprint arXiv:2410.10824},
year = {2025}
}
Comments
12 pages. arXiv admin note: text overlap with arXiv:2302.01072