%0 Journal Article
%T Rings in which elements are the sum of an
idempotent and a regular element
%J Bulletin of the Iranian Mathematical Society
%I Springer and the Iranian Mathematical Society (IMS)
%Z 1017-060X
%A Ashrafi, N.
%A Nasibi, E.
%D 2013
%\ 07/01/2013
%V 39
%N 3
%P 579-588
%! Rings in which elements are the sum of an
idempotent and a regular element
%K clean ring
%K exchange ring
%K r-clean ring
%K von Neumann regular ring
%R
%X 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
%U http://bims.iranjournals.ir/article_432_9133bb4819dd6ac2221c6ba470843a82.pdf