@article {
author = {Mohammed, Akram and Ahmed, Ibrahim and Asaad, Samah},
title = {Study of the rings in which each element express as the sum of an idempotent and pure},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {12},
number = {2},
pages = {1719-1724},
year = {2021},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {},
doi = {10.22075/ijnaa.2021.5311},
abstract = { 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 $p-\mathrm{clean\ ring}\mathrm{s}$.},
keywords = {ring,clean ring,r-clean ring,local ring and regular ring},
url = {https://ijnaa.semnan.ac.ir/article_5311.html},
eprint = {https://ijnaa.semnan.ac.ir/article_5311_6a1e25efe0449503a198d2a1eb3124aa.pdf}
}