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On a generalization of regular rings with central nilpotents | ||
| Journal of Algebra and Related Topics | ||
| دوره 14، شماره 1، آبان 2026، صفحه 37-48 اصل مقاله (169.5 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22124/jart.2025.29309.1748 | ||
| نویسندگان | ||
| Sh. Rahimi* ؛ B. Amini؛ A. Amini؛ H. Sharif | ||
| Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran | ||
| چکیده | ||
| A ring $R$ is called $\pi$-regular if, for every $x\in R$, there exists $y\in R$ such that $x^n=x^nyx^n$ for some positive integer $n$. Here, we shall give some characterizations of $\pi$-regular rings in which nilpotent elements lie in the center. It is shown that these rings can be formulated in a way motivated by recent works of P. Danchev, leading to new insights into $\pi$-regular rings and providing partial answers to a question posed by him. In the end, we aim to classify this class of rings, up to an isomorphism. | ||
| کلیدواژهها | ||
| $\pi$-regular rings؛ Von Neumann regular rings؛ Central nilpotents | ||
| مراجع | ||
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آمار تعداد مشاهده مقاله: 211 تعداد دریافت فایل اصل مقاله: 96 |
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