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 | ||
| 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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