University of Guilan Journal of Algebra and Related Topics 2345-3931 2025 06 25 On a generalization of regular rings with central nilpotents 8853 10.22124/jart.2025.29309.1748 EN Sh. Rahimi Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran B. Amini Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran A. Amini Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran H. Sharif Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran Journal Article 2024 12 20 ‎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. https://jart.guilan.ac.ir/article_8853_f648677feacf62b7408dc66d26157d00.pdf