Document Type : Research Paper

Authors

• Akram S Mohammed ¹
• Ibrahim S Ahmed ²
• Samah H Asaad ²

¹ College of Computer Science and Mathematics, Tikrit University, Tikrit, Salahaddin, Iraq

² College of Education-Tuzkhurmatu, Tikrit University, Tuzkhurmatu, Salahaddin, Iraq

Abstract

 This article aims to introduce the concept of $p-\mathrm{clean}\mathrm{ring}\mathrm{s}$ as a generalization of some concepts such as $\mathrm{clean}\mathrm{rings}$ and $r-\mathrm{clean}\mathrm{rings}$. As the first result, we prove that every $\mathrm{clean}\mathrm{ring}$ is a $p-\mathrm{clean}\mathrm{ring}$ and every $r-\mathrm{clean}\mathrm{ring}$ is a $p-\mathrm{clean}\mathrm{ring}$. Furthermore, we give the relation between von Neumann $\mathrm{local}\mathrm{ring}$ and $p-\mathrm{clean}\mathrm{ring}$. Finally,  we investigate many properties of $p-\mathrm{clean}\mathrm{ring}\mathrm{s}$.

Keywords

• ring
• clean ring
• r-clean ring
• local ring and regular ring