On $ϕ$-Prüfer like conditions

Adam Anebri; Najib Mahdou; El Houssaine Oubouhou

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arXiv · 2410.04181

On $ϕ$-Prüfer like conditions

Adam Anebri·Najib Mahdou·El Houssaine Oubouhou

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Abstract

In this paper, we investigate the question of when a $ϕ$-ring is $ϕ$-Prüfer using two types of techniques: first, by analysing the lattice structure of the nonnil ideals of $ϕ$-rings; and secondly, by considering content ideal techniques which were developed to study Gaussian polynomials. In particular, we conclude that every Gaussian $ϕ$-ring is $ϕ$-Prüfer. Key concepts such as $ϕ$-weak global dimension, primary ideals and irreducible ideals are discussed, along with their hereditary properties in $ϕ$-Prüfer rings. We also prove that any semi-local $ϕ$-Prüfer ring is a $ϕ$-Bézout ring. This paper includes several theorems and examples that provide insights into the $ϕ$-Prüfer rings and their implications in the field of ring theory.

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BibTeX RIS

Adam Anebri, Najib Mahdou, El Houssaine Oubouhou. 2024-10-05. On $ϕ$-Prüfer like conditions. https://arxiv.org/abs/2410.04181

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