On left r-clean bimodules

Author(s):

D. A. Yuwaningsih * , I. E. Wijayanti , B. Surodjo

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
‎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.‎
Keywords:

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

Language:
English
Published:
Journal of Algebra and Related Topics, Volume:11 Issue: 2, Autumn 2023
Pages:
1 to 19
https://www.magiran.com/p2671533