On Some Extensions of $π$-Regular Rings
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913347536945152 |
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| author | Danchev, Peter Javan, Arash Moussavi, Ahmad |
| author_facet | Danchev, Peter Javan, Arash Moussavi, Ahmad |
| contents | Some variations of $π$-regular and nil clean rings were recently introduced in \cite{5,8,7}, respectively. In this paper, we examine the structure and relationships between these classes of rings. Specifically, we prove that $(m, n)$-regularly nil clean rings are left-right symmetric and also show that the inclusions ($D$-regularly nil clean) $\subseteq$ (regularly nil clean) $\subseteq$ ($(m,n)$-regularly nil clean) hold, as well as we answer Questions 1, 2 and 3 posed in \cite{8}. Moreover, some other analogous questions concerning the symmetric properties of certain classes of rings are treated as well by proving that centrally Utumi rings are always strongly $π$-regular. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_06257 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Some Extensions of $π$-Regular Rings Danchev, Peter Javan, Arash Moussavi, Ahmad Rings and Algebras Representation Theory 16S34, 16U60 Some variations of $π$-regular and nil clean rings were recently introduced in \cite{5,8,7}, respectively. In this paper, we examine the structure and relationships between these classes of rings. Specifically, we prove that $(m, n)$-regularly nil clean rings are left-right symmetric and also show that the inclusions ($D$-regularly nil clean) $\subseteq$ (regularly nil clean) $\subseteq$ ($(m,n)$-regularly nil clean) hold, as well as we answer Questions 1, 2 and 3 posed in \cite{8}. Moreover, some other analogous questions concerning the symmetric properties of certain classes of rings are treated as well by proving that centrally Utumi rings are always strongly $π$-regular. |
| title | On Some Extensions of $π$-Regular Rings |
| topic | Rings and Algebras Representation Theory 16S34, 16U60 |
| url | https://arxiv.org/abs/2312.06257 |