Rings in which one-sided strongly $π$-regular elements are strongly $π$-regular
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908779908431872 |
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| author | Goyal, Dimple Rani Khurana, Dinesh |
| author_facet | Goyal, Dimple Rani Khurana, Dinesh |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_20070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings in which one-sided strongly $π$-regular elements are strongly $π$-regular Goyal, Dimple Rani Khurana, Dinesh Rings and Algebras 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. |
| title | Rings in which one-sided strongly $π$-regular elements are strongly $π$-regular |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2511.20070 |