D. A. Yuwaningsih - Department of Mathematics, Universitas Gadjah Mada , Yogyakarta, Indonesia Department of Mathematics Education, Universitas Ahmad Dahlan, Bantul, Indonesia
I. E. Wijayanti - Department Mathematics Universitas Gadjah Mada, Yogyakarta, Indonesia
B. Surodjo - Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia

‎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.‎

left r-clean, left regular element, R-bimodule, left idempotent