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Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution

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Abstract

In this paper, the authors derive the existence criteria and the formulae of the weighted Moore-Penrose inverse, the e-core inverse and the f-dual core inverse in rings. Also, new characterizations between weighted Moore-Penrose inverses and one-sided inverses along an element are given.

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Acknowledgement

The authors are highly grateful to the referees for their valuable comments and suggestions which led to improvements of this paper. In particular, Theorem 3.3 is suggested to the authors by one referee.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai University, Shanghai, 200444, China

    Huihui Zhu & Qing-Wen Wang

  2. School of Mathematics, Hefei University of Technology, Hefei, 230009, China

    Huihui Zhu

Authors
  1. Huihui Zhu
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  2. Qing-Wen Wang
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Corresponding author

Correspondence to Qing-Wen Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11971294, 11801124), China Postdoctoral Science Foundation (No. 2020M671068) and the Natural Science Foundation of Anhui Province (No. 1808085QA16).

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Zhu, H., Wang, QW. Weighted Moore-Penrose Inverses and Weighted Core Inverses in Rings with Involution. Chin. Ann. Math. Ser. B 42, 613–624 (2021). https://doi.org/10.1007/s11401-021-0282-5

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  • DOI: https://doi.org/10.1007/s11401-021-0282-5

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