On a generalization of regular rings with central nilpotents

‎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.

کلیدواژه ها:

\pi-regular rings‎ ، Von Neumann regular rings‎ ، Central nilpotents