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On left r-clean bimodules | ||
| Journal of Algebra and Related Topics | ||
| دوره 11، شماره 2، اسفند 2023، صفحه 1-19 اصل مقاله (358 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2023.24516.1525 | ||
| نویسندگان | ||
| D. A. Yuwaningsih* 1؛ I. E. Wijayanti2؛ B. Surodjo3 | ||
| 1Department of Mathematics, Universitas Gadjah Mada , Yogyakarta, Indonesia Department of Mathematics Education, Universitas Ahmad Dahlan, Bantul, Indonesia | ||
| 2Department Mathematics Universitas Gadjah Mada, Yogyakarta, Indonesia | ||
| 3Department of Mathematics, Universitas Gadjah Mada, Yogyakarta, Indonesia | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| left r-clean؛ left regular element؛ R-bimodule؛ left idempotent | ||
| مراجع | ||
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