ON LEFT r-CLEAN BIMODULES

Let R be an associative ring with identity and M an R-bimodule. We introduce the generalization of r-clean rings called left r-clean R-bimodules, defined without their endomorphism rings. An R-bimodule M is said to be left r-clean if each element is the sum of a left idempotent and a left regular element of M. We present some properties of the left r-clean R-bimodule. At the end of this paper, we give the sufficient and necessary condition for an R-bimodule to form a left r-clean R-bimodule.