[1] Zhou Yukun, Chen Jianlong,. Characterizations of m-weak group inverses [J]. Journal of Southeast University (English Edition), 2024, 40 (3): 313-318. [doi:10.3969/j.issn.1003-7985.2024.03.011]

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Characterizations of m-weak group inverses()

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

Volumn:

40

Issue:

2024 3

Page:

313-318

Research Field:

Mathematics, Physics, Mechanics

Publishing date:

2024-09-20

Info

Title:

Characterizations of m-weak group inverses

Author(s):

Zhou Yukun;  Chen Jianlong

School of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

m-weak group inverse;  weak group inverse;  Drazin inverse;  commuting property

PACS:

O151.2

DOI:

10.3969/j.issn.1003-7985.2024.03.011

Abstract:

To characterize m-weak group inverses, several algebraic methods are used, such as the use of idempotents, one-side principal ideals, and units. Consider an element a within a unitary ring that possesses Drazin invertibility and an involution. This paper begins by outlining the conditions necessary for the existence of the m-weak group inverse of a. Moreover, it explores the criteria under which a can be considered pseudo core invertible and weak group invertible. In the context of a weak proper *-ring, it is proved that a is weak group invertible if, and only if, a^D can serve as the weak group inverse of au, where u represents a specially invertible element closely associated with a^D. The paper also introduces a counterexample to illustrate that a^D cannot universally serve as the pseudo core inverse of another element. This distinction underscores the nuanced differences between pseudo core inverses and weak group inverses. Ultimately, the discussion expands to include the commuting properties of weak group inverses, extending these considerations to m-weak group inverses. Several new conditions on commuting properties of generalized inverses are given. These results show that pseudo core inverses, weak group inverses, and m-weak group inverses are not only closely linked but also have significant differences that set them apart.

References:

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Memo

Memo:

Biographies: Zhou Yukun(1996—), male, graduate; Chen Jianlong(corresponding author), male, doctor, professor, jlchen@seu.edu.cn.
Foundation items: The National Natural Science Foundation of China(No. 12171083, 12071070), Qing Lan Project of Jiangsu Province and the Postgraduate Research and Practice Innovation Program of Jiangsu Province(No. KYCX22_0231).
Citation: Zhou Yukun, Chen Jianlong.Characterizations of m-weak group inverses[J].Journal of Southeast University(English Edition), 2024, 40(3):313-318.DOI:10.3969/j.issn.1003-7985.2024.03.011.

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