Quasi sdf-absorbing ideals in commutative rings

Mathematics > Commutative Algebra Title:Quasi sdf-absorbing ideals in commutative rings View PDF HTML (experimental)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. Bibliographic and Citation Tools Code, Data and Media Associated with this Article Demos Recommenders and Search Tools arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.