%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 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