Some structural aspects of the ring of arithmetical functions: Prime ideals and beyond

Amartya Goswami; Danielle Kleyn; Kerry Porrill

doi:10.1142/S0219498826502439

Some structural aspects of the ring of arithmetical functions: Prime ideals and beyond

Amartya Goswami, Danielle Kleyn, Kerry Porrill

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

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	https://doi.org/10.1142/S0219498826502439
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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10.1142/S0219498826502439

Cite this

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KW - Arithmetic functions

KW - Dirichlet convolutions

KW - Krull dimension

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KW - prime ideal

KW - unique factorization domains

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Some structural aspects of the ring of arithmetical functions: Prime ideals and beyond

Abstract

Keywords

ASJC Scopus subject areas

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