study of the rings in which each element express as the sum of an idempotent and pure

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 $p-mathrm{clean ring}mathrm{s}$.