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arXiv · 2610.20884

Commutative rings with square-difference factor absorbing factorization

Malik Tusif Ahmed·Hwankoo Kim·Hafnaoui Hidouri·Ahmed Hamed
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Abstract

We introduce and study sdf-absorbing factorization rings (SAF-rings), in which every regular ideal is a finite product of square-difference factor absorbing ideals. We investigate their behavior under direct products, localizations, factor rings, and module idealizations, and establish connections with SP-rings, Dedekind rings, and N-rings. We also introduce strongly sdf-absorbing factorization rings (SSAF-rings), relate them to SSP-rings and almost multiplication rings, and prove that the Noetherian SSAF-rings are precisely the ZPI-rings. Applications to module idealizations and monoid rings are also presented.

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Malik Tusif Ahmed, Hwankoo Kim, Hafnaoui Hidouri, Ahmed Hamed. 2026-10-20. Commutative rings with square-difference factor absorbing factorization. https://arxiv.org/abs/2610.20884

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