@article {
author = {Ashrafi, N. and Nasibi, E.},
title = {Rings in which elements are the sum of an
idempotent and a regular element},
journal = {Bulletin of the Iranian Mathematical Society},
volume = {39},
number = {3},
pages = {579-588},
year = {2013},
publisher = {Springer and the Iranian Mathematical Society (IMS)},
issn = {1017-060X},
eissn = {1735-8515},
doi = {},
abstract = {Let R be an associative ring with unity. An element a in R is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von Neumann) element in R. If every element of R is r-clean, then R is called an r-clean ring. In this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. Further we prove that if 0 and 1 are the only idempotents in R, then an r-clean ring is an exchange ring. Also we show that the center of an r-clean ring is not necessary r-clean, but if 0 and 1 are the only idempotents in R, then the center of an r-clean ring is r-clean. Finally we give some properties and examples of r-clean rings},
keywords = {clean ring,exchange ring,r-clean ring,von Neumann regular ring},
url = {http://bims.iranjournals.ir/article_432.html},
eprint = {http://bims.iranjournals.ir/article_432_9133bb4819dd6ac2221c6ba470843a82.pdf}
}