Quasi sdf-absorbing ideals in commutative rings

TL;DR

This paper introduces quasi sdf-absorbing ideals in commutative rings, exploring their properties, stability under various constructions, and their relation to prime radicals and other ideal classes.

Contribution

It generalizes sdf-absorbing ideals, analyzes their stability, and classifies these ideals in specific rings like Z, providing new insights into their structure.

Findings

Radical of quasi sdf-absorbing ideals can be prime under certain conditions

Quasi sdf-absorption can imply sdf-absorbing primary property in specific rings

Classification of these ideals in Z and distinction from related classes

Abstract

This paper introduces and studies quasi sdf-absorbing ideals as a generalization of sdf-absorbing ideals. We investigate the stability of this property under various constructions, including localization, surjective images, Nagata idealizations, and amalgamations. We establish conditions under which the radical of such ideals is prime and discuss a specific class of rings where quasi sdf-absorption implies the sdf-absorbing primary property. The study concludes with a classification of these ideals in Z and examples distinguishing them from related ideal classes.