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arXiv · 2511.20070

Rings in which one-sided strongly $\pi$-regular elements are strongly $\pi$-regular

Dimple Rani Goyal·Dinesh Khurana
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Abstract

In 1977, Hartwig and Luh asked if $a$ is an element of a Dedekind-finite ring $S$, then does $aS = a^2S$ imply $Sa = Sa^2$. This question was answered negatively by Dittmer, Khurana, and Nielsen in 2014. On the other hand, Dittmer et al. proved that the question of Hartwig and Luh has a positive answer for Dedekind-finite exchange rings. We explore the question of Hartwig and Luh for various other classes of Dedekind-finite rings. We will also prove that the condition in question is not left-right symmetric.

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Dimple Rani Goyal, Dinesh Khurana. 2025-11-25. Rings in which one-sided strongly $\pi$-regular elements are strongly $\pi$-regular. https://arxiv.org/abs/2511.20070

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