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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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Cite

BibTeXRIS
BibTeX
@misc{ahmed2026commutative,
  title = {{Commutative rings with square-difference factor absorbing factorization}},
  author = {Malik Tusif Ahmed and Hwankoo Kim and Hafnaoui Hidouri and Ahmed Hamed},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20884},
  eprint = {2610.20884},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20884},
}
RIS
TY  - UNPB
TI  - Commutative rings with square-difference factor absorbing factorization
AU  - Malik Tusif Ahmed
AU  - Hwankoo Kim
AU  - Hafnaoui Hidouri
AU  - Ahmed Hamed
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.20884
UR  - https://arxiv.org/abs/2610.20884
AB  - 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.
ER  -