%0 Journal Article
%T Study of the rings in which each element express as the sum of an idempotent and pure
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Mohammed, Akram S
%A Ahmed, Ibrahim S
%A Asaad, Samah H
%D 2021
%\ 11/01/2021
%V 12
%N 2
%P 1719-1724
%! Study of the rings in which each element express as the sum of an idempotent and pure
%K ring
%K clean ring
%K r-clean ring
%K local ring and regular ring
%R 10.22075/ijnaa.2021.5311
%X 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 $p-\mathrm{clean\ ring}\mathrm{s}$.
%U https://ijnaa.semnan.ac.ir/article_5311_6a1e25efe0449503a198d2a1eb3124aa.pdf