On some extensions of \pi -regular rings
https://doi.org/10.26907/0021-3446-2024-10-22-33
Abstract
Some variations of \pi -regular and nil clean rings were recently introduced in the works of the first author: “A generalization of \pi -regular rings, Turkish J. Math. 43 (2), 702–711 (2019)”, “A symmetrization in \pi -regular rings, Trans. A. Razmadze Math. Inst. 174 (3), 271–275 (2020)”, “A symmetric generalization of \pi -regular rings, Ric. Mat. 73 (1), 179–190 (2024)”. 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) (regularly nil clean) ((m, n)-regularly nil clean) hold, as well as we answer Questions 1, 2 and 3 posed in the third of the above-listed works. Moreover, we also consider other similar questions concerning the symmetric properties of certain classes of rings. For example, it is proven that centrally Utumi rings are always strongly \pi -regular.
About the Authors
P. Danchev
Bulgarian Academy of Sciences
Bulgaria
Bulgaria
Peter Danchev
1113 Sofia
A. Javan
Tarbiat Modares University
Islamic Republic of Iran
Islamic Republic of Iran
Arash Javan
14115-111 Tehran Jalal AleAhmad Nasr
A. Moussavi
Tarbiat Modares University
Islamic Republic of Iran
Islamic Republic of Iran
Ahmad Moussavi
14115-111 Tehran Jalal AleAhmad Nasr
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Review
For citations:
Danchev P., Javan A., Moussavi A. On some extensions of \pi -regular rings. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika. 2024;(10):22-33. (In Russ.) https://doi.org/10.26907/0021-3446-2024-10-22-33
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