One-sided EP elements in rings with involution

• Cang Wu ^[1] ; Jianlong Chen ^[2] ; Yu Chen ^[3]
  1. [1] Nanjing Forestry University

     Nanjing Forestry University

     China

     
  2. [2] Southeast University

     Southeast University

     China

     
  3. [3] School of Electronic Science and Engineering, Hunan University of Information Technology, Republic of China

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• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 67, Nº. 2, 2024, págs. 517-528
• Idioma: inglés
• DOI: 10.33044/revuma.3572
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• Referencias bibliográficas
  • R. B. Bapat, S. K. Jain, K. M. P. Karantha, and M. D. Raj, Outer inverses: characterization and applications, Linear Algebra Appl. 528 (2017),...
  • A. Ben-Israel and T. N. E. Greville, Generalized inverses: theory and applications, second ed., CMS Books in Mathematics/Ouvrages de Mathématiques...
  • E. Boasso, On the Moore-Penrose inverse, EP Banach space operators, and EP Banach algebra elements, J. Math. Anal. Appl. 339 no. 2 (2008),...
  • W. Chen, On EP elements, normal elements and partial isometries in rings with involution, Electron. J. Linear Algebra 23 (2012), 553–561....
  • M. P. Drazin, A class of outer generalized inverses, Linear Algebra Appl. 436 no. 7 (2012), 1909–1923. DOI MR Zbl
  • M. P. Drazin, Left and right generalized inverses, Linear Algebra Appl. 510 (2016), 64–78. DOI MR Zbl
  • R. E. Hartwig, Block generalized inverses, Arch. Rational Mech. Anal. 61 no. 3 (1976), 197–251. DOI MR Zbl
  • R. E. Hartwig and K. Spindelböck, Matrices for which A∗and A\dag commute, Linear and Multilinear Algebra 14 no. 3 (1983), 241–256. DOI MR...
  • N. Jacobson, Some remarks on one-sided inverses, Proc. Amer. Math. Soc. 1 (1950), 352–355. DOI MR Zbl
  • H. Jin and J. Benitez, The absorption laws for the generalized inverses in rings, Electron. J. Linear Algebra 30 (2015), 827–842. DOI MR...
  • I. Kaplansky, Any orthocomplemented complete modular lattice is a continuous geometry, Ann. of Math. (2) 61 (1955), 524–541. DOI MR Zbl
  • J. J. Koliha, D. Djordjević, and D. Cvetković-Ilić, Moore-Penrose inverse in rings with involution, Linear Algebra Appl. 426 no. 2-3 (2007),...
  • J. J. Koliha and P. Patricio, Elements of rings with equal spectral idempotents, J. Aust. Math. Soc. 72 no. 1 (2002), 137–152. DOI MR Zbl
  • X. Liu, H. Jin, and D. Cvetković-Ilić, The absorption laws for the generalized inverses, Appl. Math. Comput. 219 no. 4 (2012), 2053–2059....
  • J. Marovt, On partial orders in proper ∗-rings, Rev. Un. Mat. Argentina 59 no. 1 (2018), 193–204. DOI MR Zbl
  • J. Marovt and D. Mosić, On some orders in ∗-rings based on the core-EP decomposition, J. Algebra Appl. 21 no. 1 (2022), Paper No. 2250010,...
  • X. Mary, On generalized inverses and Green's relations, Linear Algebra Appl. 434 no. 8 (2011), 1836–1844. DOI MR Zbl
  • D. Mosić and D. S. Djordjević, Partial isometries and EP elements in rings with involution, Electron. J. Linear Algebra 18 (2009), 761–772....
  • D. Mosić and D. S. Djordjević, Further results on partial isometries and EP elements in rings with involution, Math. Comput. Modelling 54...
  • D. Mosić and D. S. Djordjević, New characterizations of EP, generalized normal and generalized Hermitian elements in rings, Appl. Math. Comput....
  • D. Mosić, D. S. Djordjević, and J. J. Koliha, EP elements in rings, Linear Algebra Appl. 431 no. 5-7 (2009), 527–535. DOI MR Zbl
  • P. Patrício and R. Puystjens, Drazin-Moore-Penrose invertibility in rings, Linear Algebra Appl. 389 (2004), 159–173. DOI MR Zbl
  • R. Penrose, A generalized inverse for matrices, Proc. Cambridge Philos. Soc. 51 (1955), 406–413. MR Zbl
  • D. S. Rakić, N. Č. Dinčić, and D. S. Djordjević, Group, Moore-Penrose, core and dual core inverse in rings with involution, Linear Algebra...
  • H. Schwerdtfeger, Introduction to linear algebra and the theory of matrices, P. Noordhoff, Groningen, 1950. MR Zbl
  • C. Wu and J. Chen, Left core inverses in rings with involution, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 116 no. 2 (2022),...
  • S. Xu, J. Chen, and J. Benítez, EP elements in rings with involution, Bull. Malays. Math. Sci. Soc. 42 no. 6 (2019), 3409–3426. DOI MR ...
  • H. Zhu, J. Chen, and P. Patrício, Further results on the inverse along an element in semigroups and rings, Linear Multilinear Algebra 64 no....