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.
Rahimi, S. , Amini, B. , Amini, A. and Sharif, H. (2025). On a generalization of regular rings with central nilpotents. Journal of Algebra and Related Topics, (), -. doi: 10.22124/jart.2025.29309.1748
MLA
Rahimi, S. , , Amini, B. , , Amini, A. , and Sharif, H. . "On a generalization of regular rings with central nilpotents", Journal of Algebra and Related Topics, , , 2025, -. doi: 10.22124/jart.2025.29309.1748
HARVARD
Rahimi, S., Amini, B., Amini, A., Sharif, H. (2025). 'On a generalization of regular rings with central nilpotents', Journal of Algebra and Related Topics, (), pp. -. doi: 10.22124/jart.2025.29309.1748
CHICAGO
S. Rahimi , B. Amini , A. Amini and H. Sharif, "On a generalization of regular rings with central nilpotents," Journal of Algebra and Related Topics, (2025): -, doi: 10.22124/jart.2025.29309.1748
VANCOUVER
Rahimi, S., Amini, B., Amini, A., Sharif, H. On a generalization of regular rings with central nilpotents. Journal of Algebra and Related Topics, 2025; (): -. doi: 10.22124/jart.2025.29309.1748
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