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A note on mj-clean rings | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 15، دوره 15، شماره 10، دی 2024، صفحه 175-179 اصل مقاله (356.51 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.30963.4528 | ||
| نویسندگان | ||
| Mehrdad Esfandiar1؛ Hamid Haj Seyyed Javadi* 2؛ Ahmad Moussavi3 | ||
| 1Department of Mathematics, Shahed University, Tehran, Iran | ||
| 2Department of Computer Engineering, Shahed University, Tehran, Iran | ||
| 3Department of Pure Mathematics, Tarbiat Modares, Tehran, Iran | ||
| تاریخ دریافت: 25 خرداد 1402، تاریخ پذیرش: 01 مهر 1402 | ||
| چکیده | ||
| In this paper, we examine the notions of $mj$-clean ring and strongly $mj$-clean ring. And we will provide some of its basic properties. We examine the relationship of $mj$-clean ring with $m$-clean ring and $j$-clean ring. We prove that $R$ is strongly $mj$-clean ring if and only if $M_n(R)$ is strongly $mj$-clean ring. We prove that $mj$-clean ring is Dedekind-finite; i.e., $ab=1$ implies that $ba=1$. | ||
| کلیدواژه‌ها | ||
| mj-clean ring؛ strongly mj-clean ring؛ Dedekind finite | ||
| مراجع | ||
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