[1] Zhu Huihui, Chen Jianlong,. Representations of the Drazin inverseinvolving idempotents in a ring [J]. Journal of Southeast University (English Edition), 2015, 31 (3): 427-430. [doi:10.3969/j.issn.1003-7985.2015.03.023]

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Representations of the Drazin inverseinvolving idempotents in a ring()

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Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:

31

Issue:

2015 3

Page:

427-430

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2015-09-20

Info

Title:

Representations of the Drazin inverseinvolving idempotents in a ring

Author(s):

Zhu Huihui;  Chen Jianlong

Department of Mathematics, Southeast University, Nanjing 211189, China

Keywords:

idempotent;  Drazin inverse;  spectral idempotent

PACS:

O151.2

DOI:

10.3969/j.issn.1003-7985.2015.03.023

Abstract:

An element a of a ring R is called Drazin invertible if there exists b∈R such that ab=ba, bab=b, and a-a²b is nilpotent. The element b above is unique if it exists and is denoted as a^D. The equivalent conditions of the Drazin inverse involving idempotents in R are established. As applications, some formulae for the Drazin inverse of the difference and the product of idempotents in a ring are given. Hence, a number of results of bounded linear operators in Banach spaces are extended to the ring case.

References:

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Memo

Memo:

Biographies: Zhu Huihui(1985─), male, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No.11371089), the Specialized Research Fund for the Doctoral Program of Higher Education(No.20120092110020), the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX13-072), the Scientific Research Foundation of Graduate School of Southeast University, the Fundamental Research Funds for the Central Universities(No.22420135011).
Citation: Zhu Huihui, Chen Jianlong. Representations of the Drazin inverse involving idempotents in a ring[J].Journal of Southeast University(English Edition), 2015, 31(3):427-430.[doi:10.3969/j.issn.1003-7985.2015.03.023]

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