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Study of the rings in which each element express as the sum of an idempotent and pure | ||
| International Journal of Nonlinear Analysis and Applications | ||
| دوره 12، شماره 2، بهمن 2021، صفحه 1719-1724 اصل مقاله (325.56 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.5311 | ||
| نویسندگان | ||
| Akram S Mohammed1؛ Ibrahim S Ahmed* 2؛ Samah H Asaad2 | ||
| 1College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq | ||
| 2College of Education-Tuzkhurmatu, Tikrit University, Tuzkhurmatu, Salahaddin, Iraq | ||
| تاریخ دریافت: 03 فروردین 1400، تاریخ بازنگری: 19 فروردین 1400، تاریخ پذیرش: 15 خرداد 1400 | ||
| چکیده | ||
| This article aims to introduce the concept of $p-\mathrm{clean\ ring}\mathrm{s}$ as a generalization of some concepts such as $\mathrm{clean\ rings}$ and $r-\mathrm{clean\ rings}$. As the first result, we prove that every $\mathrm{clean\ ring}$ is a $p-\mathrm{clean\ ring}$ and every $r-\mathrm{clean\ ring}$ is a $p-\mathrm{clean\ ring}$. Furthermore, we give the relation between von Neumann $\mathrm{local\ ring}$ and $p-\mathrm{clean\ ring}$. Finally, we investigate many properties of $p-\mathrm{clean\ ring}\mathrm{s}$. | ||
| کلیدواژهها | ||
| ring؛ clean ring؛ r-clean ring؛ local ring and regular ring | ||
| مراجع | ||
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[1] A. Andari, The relationships between clean rings, r-clean rings, and f-clean rings, AIP Con. Proc. 2021(1) (2018) 1–4. [2] D. F. Anderson and A. Badawi, Von neumann regular and related elements in commutative rings, Algebra Colloq. 19(spec01) (2012) 1017–1040. [3] N. Ashrafi and E. Nasibi, Rings in which elements are the sum of an idempotent and a regular element, Bull. Iran. Math. Soc. 39(3) (2013) 579–588. [4] N. Ashrafi and E. Nasibi, r-CLEAN RINGS, Math. Rep. 15(65) (2013) 125–132. [5] W. Chen and S. Cui, On Clean Rings and Glean Elements, Southeast Asian Bull. Math. 32(5) (2008) 855–861. [6] F. D. de Melo Hern´andez, C. A. Hern´andez Melo and H. Tapia-Recillas, On idempotents of a class of commutative rings, Commun. Algebra 48(9) (2020) 4013–4026. [7] M. A. Goldman, Ring theory, Nature, 432(7018) (2004) 674–675. [8] W. K. Nicholson, Lifting idempotents and exchange rings, Trans. Amer. Math. Soc. 229 (1977) 269. [9] L. Vaˇs, *-clean rings; some clean and almost clean Baer *-rings and von Neumann algebras, J. Algebra 324(12) (2010) 3388–3400. [10] A. Wardayani, I. Kharismawati and I. Sihwaningrum, Regular rings and their properties, J. Phys: Conf. Ser. 1494(1) (2020). | ||
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