English

Some remarks on the ring of arithmetical functions

Rings and Algebras 2024-09-24 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 show arithmetic ring has infinite Krull dimension and its associated prime ideal set is nonempty.

Keywords

Cite

@article{arxiv.2302.01072,
  title  = {Some remarks on the ring of arithmetical functions},
  author = {Amartya Goswami},
  journal= {arXiv preprint arXiv:2302.01072},
  year   = {2024}
}

Comments

The paper contains some incorrect results

R2 v1 2026-06-28T08:30:14.800Z