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arXiv · 2410.10824

On structures of the ring of arithmetical functions: prime ideals and beyond

Amartya Goswami·Danielle Kleyn·Kerry Porrill
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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.

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Amartya Goswami, Danielle Kleyn, Kerry Porrill. 2024-09-20. On structures of the ring of arithmetical functions: prime ideals and beyond. https://arxiv.org/abs/2410.10824

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