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[1] Li Wende, Chen Jianlong,. Centrally clean elements and central Drazin inverses in a ring [J]. Journal of Southeast University (English Edition), 2022, 38 (3): 315-322. [doi:10.3969/j.issn.1003-7985.2022.03.014]
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Centrally clean elements and central Drazin inverses in a ring()
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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
38
Issue:
2022 3
Page:
315-322
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2022-09-20

Info

Title:
Centrally clean elements and central Drazin inverses in a ring
Author(s):
Li Wende;  Chen Jianlong
School of Mathematics, Southeast University, Nanjing 211189, China
Keywords:
centrally clean element;  centrally clean ring;  central Drazin inverse;  central group inverse
PACS:
O153.3
DOI:
10.3969/j.issn.1003-7985.2022.03.014
Abstract:
Element a in ring R is called centrally clean if it is the sum of central idempotent e and unit u. Moreover, a=e+u is called a centrally clean decomposition of a and R is called a centrally clean ring if every element of R is centrally clean. First, some characterizations of centrally clean elements are given. Furthermore, some properties of centrally clean rings, as well as the necessary and sufficient conditions for R to be a centrally clean ring are investigated. Centrally clean rings are closely related to the central Drazin inverses. Then, in terms of centrally clean decomposition, the necessary and sufficient conditions for the existence of central Drazin inverses are presented. Moreover, the central cleanness of special rings, such as corner rings, the ring of formal power series over ring R, and a direct product ∏Rα of ring Rα, is analyzed. Furthermore, the central group invertibility of combinations of two central idempotents in the algebra over a field is investigated. Finally, as an application, an example that lists all invertible, central group invertible, group invertible, central Drazin invertible elements, and centrally clean elements of the group ring Z2S3 is given.

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Memo

Memo:
Biographies: Li Wende(1993—), male, Ph.D. candidate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No. 12171083, 11871145, 12071070), the Qing Lan Project of Jiangsu Province.
Citation: Li Wende, Chen Jianlong. Centrally clean elements and central Drazin inverses in a ring[J].Journal of Southeast University(English Edition), 2022, 38(3):315-322.DOI:10.3969/j.issn.1003-7985.2022.03.014.
Last Update: 2022-09-20