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Journals / International Electronic Journal of Algebra / 2026 / Volume: 40 Issue: 40

G-outer inverses and partial orders in rings

Marija Petrovic(University of Nis)
Pages
—
Publication Date
2026-07-16
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Consequently, one-sided G-Drazin inverses are introduced for elements of a ring as well as partial orders induced by them.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The notions of G-outer inverse and its one-sided versions for rectangular complex matrices are generalized to elements of a ring based on the $(b,c)$-inverse.
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Key Findings & Data:Various properties and characterizations of G-outer inverse and its one-sided kinds are developed.
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Conclusion & Impact:Consequently, one-sided G-Drazin inverses are introduced for elements of a ring as well as partial orders induced by them.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$(b · c)$-inverse · G-outer inverse

Abstract

The notions of G-outer inverse and its one-sided versions for rectangular complex matrices are generalized to elements of a ring based on the $(b,c)$-inverse. Various properties and characterizations of G-outer inverse and its one-sided kinds are developed. We consider partial orders applying G-outer inverse and its one-sided types in a ring. Consequently, one-sided G-Drazin inverses are introduced for elements of a ring as well as partial orders induced by them.

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Cite This Article

Petrovic, M. (2026). G-outer inverses and partial orders in rings. International Electronic Journal of Algebra, Volume: 40 Issue: 40. https://doi.org/10.24330/ieja.1925631

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References (17)

  1. C. Coll, M. Lattanzi and N. Thome, Weighted G-Drazin inverses and a new pre-order on rectangular matrices, Appl. Math. Comput., 317 (2018), 12-24.
  2. G. Dolinar, B. Kuzma, J. Marovt and D. Mosic, On G-Drazin partial order in rings, Acta Math. Hungar., 173 (2024), 176-192.
  3. M. P. Drazin, A class of outer generalized inverses, Linear Algebra Appl., 436 (2012), 1909-1923.
  4. D. E. Ferreyra, M. Lattanzi, F. E. Levis and N. Thome, Parametrized solutions $X$ of the system $AXA=AEA$ and $A^kEAX=XAEA^k$ for a matrix $A$ having index $k$, Electron. J. Linear Algebra, 35 (2019), 503-510.
  5. D. E. Ferreyra, M. Lattanzi, F. E. Levis and N. Thome, Solving an open problem about the G-Drazin partial order, Electron. J. Linear Algebra, 36 (2020), 55-66.
  6. R. E. Hartwig, How to partially order regular elements, Math. Japon., 25 (1980), 1-13.
  7. G. Maharana, J. K. Sahoo and N. Thome, G-Drazin inverse combined with inner inverse, Linear Multilinear Algebra, 73(1) (2025), 106-121.
  8. D. Mosic, Weighted G-Drazin inverse for operators on Banach spaces, Carpathian J. Math., 35(2) (2019), 171-184.
  9. D. Mosic, G-outer inverse of Banach spaces operators, J. Math. Anal. Appl., 481 (2020), 123501 (15 pp).
  10. D. Mosic, Solvability to some systems of matrix equations using G-outer inverses, Electron. J. Linear Algebra, 36 (2020), 265-276.
  11. D. Mosic and L. Wang, Left and right G-outer inverses, Linear Multilinear Algebra, 70(17) (2022), 3319-3344.
  12. P. S. Stanimirovic, S. D. Mourtas, D. Mosic, V. N. Katsikis, X. Cao and S. Li, A zeroing neural network approach for calculating time-varying G-outer inverse of arbitrary matrix, IEEE Trans. Neural Netw. Learn. Syst., 36(5) (2025), 8843-8852.
  13. J. Visnjic, I. Stanisev and Y. Ke, Some properties of (b,c)-inverses in rings, Comm. Algebra, 51(6) (2023), 2600-2613.
  14. L. Wang, J. Chen and N. Castro-Gonzalez, Characterizations of the $(b,c)$-inverse in a ring, arXiv:1507.01446 [math.RA] (2015).
  15. H. Wang and X. Liu, Partial orders based on core-nilpotent decomposition, Linear Algebra Appl., 488 (2016), 235-248.
  16. C. Wu and J. Chen, Strongly one-sided (b,c)-inverses in rings, Algebra Colloq., 31(4) (2024), 549-558.
  17. S. Xu and J. Benitez, Existence criteria and expressions of the (b,c)-inverse in rings and their applications, Mediterr. J. Math., 15(1) (2018), 14 (11 pp).