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Equivalence Relations Based on (b,c)-Inverses in Rings

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Abstract

In this paper, we introduce a binary relation in the set of all (b, c)-invertible elements of a ring, defined in the manner like minus, star, sharp, core, and dual core partial orders. We prove that this binary relation is actually an equivalence relation and we investigate some of its properties. Furthermore, we define another equivalence relation on the set of all (b, c)-invertible elements of a ring, as an improvement of the previous mentioned equivalence relation. In addition, the equivalence criteria are given for the equality of (b, c)-related idempotents of two elements and their (b, c)-invertibility is studied.

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Acknowledgements

The authors wish to thank the anonymous referees for their useful comments which greatly improved the presentation of this paper.

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Authors and Affiliations

  1. Technical Faculty in Bor, University of Belgrade, Vojske Jugoslavije 12, 19210, Bor, Serbia

    Ivana Stanišev

  2. Faculty of Medicine, University of Niš, Bulevar dr Zorana Djindjića 81, 18108, Niš, Serbia

    Jelena Višnjić

  3. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, P.O. Box 95, 18000, Niš, Serbia

    Dragan S. Djordjević

Authors
  1. Ivana Stanišev
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  2. Jelena Višnjić
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  3. Dragan S. Djordjević
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Contributions

Ivana Stanišev and Jelena Višnjić wrote the main manuscript text. Dragan Djordjević supervised and reviewed the work.

Corresponding author

Correspondence to Dragan S. Djordjević.

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The authors have no conflicts of interest to declare.

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I. Stanišev: Supported by Grant No. 451-03-47/2023-01/200131 of the Ministry of Education, Science and Technological Development, Republic of Serbia

J. Višnjić: Supported by Grant No. 451-03-47/2023-01/200113 of the Ministry of Education, Science and Technological Development, Republic of Serbia

D. S. Djordjević: Supported by Grant No. 451-03-47/2023–01/200124 of the Ministry of Education, Science and Technological Development, Republic of Serbia.

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Stanišev, I., Višnjić, J. & Djordjević, D.S. Equivalence Relations Based on (b,c)-Inverses in Rings. Mediterr. J. Math. 21, 11 (2024). https://doi.org/10.1007/s00009-023-02545-5

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  • DOI: https://doi.org/10.1007/s00009-023-02545-5

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