On P -Clean Rings
DOI:
https://doi.org/10.29304/jqcm.2022.14.2.949Keywords:
clean ring, r-clean ring, strongly r-clean ringAbstract
If all the elements of a ring W can be written as a sum of pure and idempotent elements", the ring is said to be P-clean. In this paper, we introduce the P-clean ring nation and look into some of its fundamental properties, examples, and relationship to the clean ring
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References
[1] Andari, Ari. "The relationships between clean rings, r-clean rings, and f-clean rings." AIP Conference Proceedings. Vol. 2021. No. 1. AIP Publishing LLC, 2018.
[2] Ashrafi, Nahid, and Ebrahim Nasibi. "r-clean rings." arXiv preprint arXiv:1104.2167 (2011).
[3] Ashrafi, N. A. H. I. D., and E. B. R. A. H. I. M. Nasibi. "Rings in which elements are the sum of an idempotent and a regular element." Bulletin of the Iranian Mathematical Society 39.3 (2013): 579-588.
[4] Chen, Weixing. "Notes on Clean Rings and Clean elements." Southeast Asian Bulletin of Mathematics 2998.32: 00-6.
[5] Mohammed, Akram S., Ibrahim S. Ahmed, and Samah H. Asaad. "Study of the rings in which each element express as the sum of an idempotent and pure." International Journal of Nonlinear Analysis and Applications 12.2 (2021): 1719-1724.
[6] Nicholson .W.K., ''Lifting idempotent and exchange rings'', Trans. Amer. Math. Soc., 229(1977), 269-278 .
[7] Sabet, SH A. Safari, M. Farmani, and M. Karami. "π-Clean and strongly π-clean rings." Measurement 109 (2017): 74-78.
[8] Sharma, Ajay, and Dhiren Kumar Basnet. "Weakly r-clean rings and weakly⋆-clean rings." arXiv preprint arXiv:1702.06734 (2017).
[9] Sharma, Garima, and Amit B. Singh. "Strongly r-clean Rings." International Journal of Mathematics and Computer Science 13 (2018): 207-214.
[2] Ashrafi, Nahid, and Ebrahim Nasibi. "r-clean rings." arXiv preprint arXiv:1104.2167 (2011).
[3] Ashrafi, N. A. H. I. D., and E. B. R. A. H. I. M. Nasibi. "Rings in which elements are the sum of an idempotent and a regular element." Bulletin of the Iranian Mathematical Society 39.3 (2013): 579-588.
[4] Chen, Weixing. "Notes on Clean Rings and Clean elements." Southeast Asian Bulletin of Mathematics 2998.32: 00-6.
[5] Mohammed, Akram S., Ibrahim S. Ahmed, and Samah H. Asaad. "Study of the rings in which each element express as the sum of an idempotent and pure." International Journal of Nonlinear Analysis and Applications 12.2 (2021): 1719-1724.
[6] Nicholson .W.K., ''Lifting idempotent and exchange rings'', Trans. Amer. Math. Soc., 229(1977), 269-278 .
[7] Sabet, SH A. Safari, M. Farmani, and M. Karami. "π-Clean and strongly π-clean rings." Measurement 109 (2017): 74-78.
[8] Sharma, Ajay, and Dhiren Kumar Basnet. "Weakly r-clean rings and weakly⋆-clean rings." arXiv preprint arXiv:1702.06734 (2017).
[9] Sharma, Garima, and Amit B. Singh. "Strongly r-clean Rings." International Journal of Mathematics and Computer Science 13 (2018): 207-214.
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Published
2022-06-14
How to Cite
Ramzib, E. H., & Mohammed, A. S. (2022). On P -Clean Rings. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(2), Math Page 46–53. https://doi.org/10.29304/jqcm.2022.14.2.949
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Math Articles
