Study of the rings in which each element express as the sum of an idempotent and pure
نویسندگان
1 College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq
2 College of Education-Tuzkhurmatu, Tikrit University, Tuzkhurmatu, Salahaddin, Iraq
3 College of Education-Tuzkhurmatu, Tikrit University, Tuzkhurmatu, Salahaddin, Iraq
doi
10.22075/ijnaa.2021.5311چکیده
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 $p-\mathrm{clean\ ring}\mathrm{s}$.
