On left r-clean bimodules

Document Type : Research Paper

Authors

1 Department of Mathematics, Universitas Gadjah Mada , Yogyakarta, Indonesia Department of Mathematics Education, Universitas Ahmad Dahlan, Bantul, Indonesia

2 Department Mathematics Universitas Gadjah Mada, Yogyakarta, Indonesia

3 Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia

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.‎

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Journal of Algebra and Related Topics
Volume 11, Issue 2
December 2023
Pages 1-19

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