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arXiv · 2302.01072

Some remarks on the ring of arithmetical functions

Amartya Goswami
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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 show arithmetic ring has infinite Krull dimension and its associated prime ideal set is nonempty.

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Amartya Goswami. 2023-02-02. Some remarks on the ring of arithmetical functions. https://arxiv.org/abs/2302.01072

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