TY - JOUR
ID - 432
TI - Rings in which elements are the sum of an
idempotent and a regular element
JO - Bulletin of the Iranian Mathematical Society
JA - BIMS
LA - en
SN - 1017-060X
AU - Ashrafi, N.
AU - Nasibi, E.
AD - Semnan University
Y1 - 2013
PY - 2013
VL - 39
IS - 3
SP - 579
EP - 588
KW - clean ring
KW - exchange ring
KW - r-clean ring
KW - von Neumann regular ring
DO -
N2 - 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
UR - http://bims.iranjournals.ir/article_432.html
L1 - http://bims.iranjournals.ir/article_432_9133bb4819dd6ac2221c6ba470843a82.pdf
ER -